Laws of Exponents Quiz (10/22): every problem, solved
Algebra I · Mr. Naipaul and Mr. Clark · Version A and Version B
How to use these slides
- Try each problem on paper first.
- Stuck? Press Show the next step. Each step names the law it uses and says why.
- Still stuck? Watch the Khan Academy video on the slide, then revise your own answer.
Which version is your quiz? It says Version A or Version B at the top.
Every problem
- Problem 1Power of a power · product of powers 4 points
- Problem 2Quotient of powers 6 points
- Problem 3Quotient of powers 3 points
- Problem 4Negative exponent 3 points
- Problem 5Power of a product · power of a power 4 points
- Problem 6Power of a power 6 points
- Problem 7Power of a power 3 points
- Problem 8Power of a product · power of a power 8 points
- Problem 9Power of a product 3 points
- Problem 10Power of a quotient · power of a power 8 points
- Problem 11Power of a quotient 3 points
- Problem 12Zero exponent 3 points
- Problem 13Power of a power · quotient of powers 5 points
- Problem 14Product of powers · quotient of powers · negative exponent 6 points
Problem 1
4 pointsPower of a power · product of powersSelect all true statements about the expression m3·(m4)2. Circle the letter of every true statement. Write your final choices in the answer box.
Try it first on paper. Then check one step at a time.
- Step 1False(a) (m4)2·m3=
m6·m3 Power of a power: multiply the exponents, so (m4)2=
m8 , not m6 (that adds 4+2 ). - Step 2True(b) (m4)2·m3=
m8·m3 Power of a power: (m4)2=
m4·2= , and the factor m3 does not change.m8 - Step 3True(c) m3·(m4)2=
(m4)2·m3 Commutative property: changing the order of two factors does not change the product.
- Step 4False(d) m6·m3=
m18 Product of powers: same base, multiplying, so add the exponents: m6·m3=
m9 , not m18 (that multiplies 6·3). - Step 5False(e) m3·m6=
m18 Product of powers: m3·m6=
m3+6= , so m18 is false.m9 - Step 6True(f) m8·m3=
m11 Product of powers: same base, multiplying, so add the exponents: 8+
3= .11 - Step 7False(g) m8·m3=
m24 Product of powers adds the exponents: m8·m3=
m11 , not m24 (that multiplies 8·3). - Step 8True(h) (m4)2·m3=
m11 Both laws in order: the power of a power gives (m4)2=
m8 , then the product of powers gives m8·m3=m11 .
Answer
Written as: the letters of every true statement
The trap
A common wrong answer: (g) m8·m3=
Circling (g) multiplies the exponents (8·3=
Select all true statements about the expression (n5)2·n4. Circle the letter of every true statement. Write your final choices in the answer box.
Try it first on paper. Then check one step at a time.
- Step 1True(a) n4·(n5)2=
n4·n10 Power of a power: (n5)2=
n5·2= , and the factor n4 does not change.n10 - Step 2False(b) n4·(n5)2=
n4·n7 Power of a power: multiply the exponents, so (n5)2=
n10 , not n7 (that adds 5+2 ). - Step 3False(c) n7·n4=
n28 Product of powers: same base, multiplying, so add the exponents: n7·n4=
n11 , not n28 (that multiplies 7·4). - Step 4True(d) (n5)2·n4=
n4·(n5)2 Commutative property: changing the order of two factors does not change the product.
- Step 5True(e) n4·(n5)2=
n14 Both laws in order: the power of a power gives (n5)2=
n10 , then the product of powers gives n4·n10=n14 . - Step 6False(f) n4·n7=
n28 Product of powers: n4·n7=
n4+7= , so n28 is false.n11 - Step 7True(g) n4·n10=
n14 Product of powers: same base, multiplying, so add the exponents: 4+
10= .14 - Step 8False(h) n4·n10=
n40 Product of powers adds the exponents: n4·n10=
n14 , not n40 (that multiplies 4·10).
Answer
Written as: the letters of every true statement
The trap
A common wrong answer: (h) n4·n10=
Circling (h) multiplies the exponents (4·10=
Watch it explained
Exponent properties 1 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy product of powers exponents"
Now revise: On your quiz, circle exactly the true letters, (b), (c), (f), (h), and write them in the answer box. Next to each false statement, write what its right side should be.
Now revise: On your quiz, circle exactly the true letters, (a), (d), (e), (g), and write them in the answer box. Next to each false statement, write what its right side should be.
Problem 2
6 pointsQuotient of powersCircle one choice in each row. Write your final choices in the answer box.
I can … the … because …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
I can (d) subtract
Quotient of powers: when you divide two powers with the same base, you subtract the exponents.
- Step 2
the (b) exponents
Quotient of powers: only the exponents change; the base 8 stays 8.
- Step 3
because (c) the bases are the same and I am dividing two powers
The quotient of powers applies because both powers have the base 8 and the fraction bar means division.
- Step 4
so the answer is (b) 812
81886=818−6= 812 Subtract: 18−
6= , because the 6 factors of 8 on the bottom cancel 6 of the 18 on top; that is choice (b).12
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) 83
Choice (a) divides the exponents (18÷6=
Circle one choice in each row. Write your final choices in the answer box.
I can … the … because …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
I can (d) subtract
Quotient of powers: when you divide two powers with the same base, you subtract the exponents.
- Step 2
the (b) exponents
Quotient of powers: only the exponents change; the base 6 stays 6.
- Step 3
because (c) the bases are the same and I am dividing two powers
The quotient of powers applies because both powers have the base 6 and the fraction bar means division.
- Step 4
so the answer is (c) 615
62065=620−5= 615 Subtract: 20−
5= , because the 5 factors of 6 on the bottom cancel 5 of the 20 on top; that is choice (c).15
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) 64
Choice (a) divides the exponents (20÷5=
Watch it explained
Exponent properties involving quotients (examples) | 8th grade | Khan Academy
Video by Khan Academy
Open on YouTube · Khan Academy lesson page
If the video will not play, search Google for: "Khan Academy quotient of powers exponents"
Now revise: On your quiz, circle the right choice in every row and write all 4 letters in the answer box.
Now revise: On your quiz, circle the right choice in every row and write all 4 letters in the answer box.
Problem 3
3 pointsQuotient of powersWrite as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 172177=
721−7 Quotient of powers: the bases are the same and you are dividing, so subtract the exponents, top minus bottom.
- Step 2=
714 21−
7= , and the base stays 7: the 7 factors of 7 on the bottom cancel 7 on top.14
Answer
Written as: a single power
The trap
A common wrong answer: 73
73 divides the exponents (21÷7=
Write as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 151452=
514−2 Quotient of powers: the bases are the same and you are dividing, so subtract the exponents, top minus bottom.
- Step 2=
512 14−
2= , and the base stays 5: the 2 factors of 5 on the bottom cancel 2 on top.12
Answer
Written as: a single power
The trap
A common wrong answer: 57
57 divides the exponents (14÷2=
Watch it explained
Exponent properties involving quotients (examples) | 8th grade | Khan Academy
Video by Khan Academy
Open on YouTube · Khan Academy lesson page
If the video will not play, search Google for: "Khan Academy quotient of powers exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Problem 4
3 pointsNegative exponentEvaluate. Write as a fraction. Show your work.
Try it first on paper. Then check one step at a time.
- Step 13·2−4=
3·124 Negative exponent: 2−4 is the reciprocal of 24, and only the 2 carries the exponent, so the 3 does not move.
- Step 2=
324 Multiplying 3 by 124 puts the 3 in the numerator.
- Step 3=
316 24=
2·2·2·2= , so the answer is the fraction 316, a positive number.16
Answer
Written as: a fraction
The trap
A common wrong answer: 148
148 moves the 3 to the bottom as well, but only the 2 carries the negative exponent: the 3 stays on top.
Evaluate. Write as a fraction. Show your work.
Try it first on paper. Then check one step at a time.
- Step 15·3−2=
5·132 Negative exponent: 3−2 is the reciprocal of 32, and only the 3 carries the exponent, so the 5 does not move.
- Step 2=
532 Multiplying 5 by 132 puts the 5 in the numerator.
- Step 3=
59 32=
3·3= , so the answer is the fraction 59, a positive number.9
Answer
Written as: a fraction
The trap
A common wrong answer: 145
145 moves the 5 to the bottom as well, but only the 3 carries the negative exponent: the 5 stays on top.
Watch it explained
Negative exponents | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy
Video by Khan Academy
Open on YouTube · Khan Academy lesson page
If the video will not play, search Google for: "Khan Academy negative exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a fraction.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a fraction.
Problem 5
4 pointsPower of a product · power of a powerWrite the letter of the equivalent expression in the box.
Which expression is equivalent to (2x3y)4?
Try it first on paper. Then check one step at a time.
- Step 1(2x3y)4=
24·(x3)4·y4 Power of a product: the power 4 goes on every factor inside the parentheses: the 2, the x3 and the y.
- Step 2=
16·(x3)4·y4 The coefficient is raised to the power too: 24=
2·2·2·2= , not 2·4=16 8 . - Step 3=
16x12y4 Power of a power: multiply the exponents, 3·4=
12 , so (x3)4=x12 . - Step 4
(d) 16x12y4
Choice (d) is 16x12y4, the same expression.
Answer
Written as: the letter of the equivalent expression
The trap
A common wrong answer: (b) 8x12y4
Choice (b) multiplies the coefficient by the exponent (2·4=
Write the letter of the equivalent expression in the box.
Which expression is equivalent to (3m2n)3?
Try it first on paper. Then check one step at a time.
- Step 1(3m2n)3=
33·(m2)3·n3 Power of a product: the power 3 goes on every factor inside the parentheses: the 3, the m2 and the n.
- Step 2=
27·(m2)3·n3 The coefficient is raised to the power too: 33=
3·3·3= , not 3·3=27 9 . - Step 3=
27m6n3 Power of a power: multiply the exponents, 2·3=
6 , so (m2)3=m6 . - Step 4
(a) 27m6n3
Choice (a) is 27m6n3, the same expression.
Answer
Written as: the letter of the equivalent expression
The trap
A common wrong answer: (c) 9m6n3
Choice (c) multiplies the coefficient by the exponent (3·3=
Watch it explained
Exponent properties 5 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a product exponents"
Now revise: On your quiz, write the steps that lead to the answer, then write the letter (d) in the box.
Now revise: On your quiz, write the steps that lead to the answer, then write the letter (a) in the box.
Problem 6
6 pointsPower of a powerCircle one choice in each row. Write your final choices in the answer box.
I can … the … because …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
I can (b) multiply
Power of a power: when a power is raised to another power, you multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base y stays y.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because y4 is inside the parentheses and 7 is the power outside them.
- Step 4
so the answer is (a) y28
(y4)7=y4·7= y28 Multiply: 4·7=
28 (7 groups of 4 factors of y), so choice (a).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (b) y11
Choice (b) adds the exponents (4+
Circle one choice in each row. Write your final choices in the answer box.
I can … the … because …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
I can (b) multiply
Power of a power: when a power is raised to another power, you multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base k stays k.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because k6 is inside the parentheses and 5 is the power outside them.
- Step 4
so the answer is (d) k30
(k6)5=k6·5= k30 Multiply: 6·5=
30 (5 groups of 6 factors of k), so choice (d).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) k11
Choice (a) adds the exponents (6+
Watch it explained
Exponent properties 3 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a power exponents"
Now revise: On your quiz, circle the right choice in every row and write all 4 letters in the answer box.
Now revise: On your quiz, circle the right choice in every row and write all 4 letters in the answer box.
Problem 7
3 pointsPower of a powerWrite as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 1(k3)9=
k3·9 Power of a power: a power raised to another power keeps the base and multiplies the exponents.
- Step 2=
k27 3·9=
27 : 9 groups of 3 factors of k.
Answer
Written as: a single power
The trap
A common wrong answer: k12
k12 adds the exponents (3+
Write as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 1(r2)9=
r2·9 Power of a power: a power raised to another power keeps the base and multiplies the exponents.
- Step 2=
r18 2·9=
18 : 9 groups of 2 factors of r.
Answer
Written as: a single power
The trap
A common wrong answer: r11
r11 adds the exponents (2+
Watch it explained
Exponent properties 3 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a power exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Problem 8
8 pointsPower of a product · power of a powerCircle one choice in each row. Write your final choices in the answer box.
For x5, I can … the … because …; for the coefficient 3, I can …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
For x5, I can (b) multiply
Power of a power: x5 raised to the power 3 means multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base x stays x.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because x5 is inside the parentheses and 3 is the power outside them.
- Step 4
For the coefficient 3, I can (c) raise it to the power 3
Power of a product: the power 3 goes on every factor inside the parentheses, so the coefficient 3 is raised to the power 3 too.
- Step 5
so the answer is (c) 27x15
(3x5)3=33·x5·3= 27x15 Power of a product with a power of a power: 33=
27 and 5·3=15 , so choice (c).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) 9x15
Choice (a) multiplies the coefficient by the exponent (3·3=
Circle one choice in each row. Write your final choices in the answer box.
For y6, I can … the … because …; for the coefficient 2, I can …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
For y6, I can (b) multiply
Power of a power: y6 raised to the power 4 means multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base y stays y.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because y6 is inside the parentheses and 4 is the power outside them.
- Step 4
For the coefficient 2, I can (c) raise it to the power 4
Power of a product: the power 4 goes on every factor inside the parentheses, so the coefficient 2 is raised to the power 4 too.
- Step 5
so the answer is (b) 16y24
(2y6)4=24·y6·4= 16y24 Power of a product with a power of a power: 24=
16 and 6·4=24 , so choice (b).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) 8y24
Choice (a) multiplies the coefficient by the exponent (2·4=
Watch it explained
Exponent properties 5 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a product exponents"
Now revise: On your quiz, circle the right choice in every row and write all 5 letters in the answer box.
Now revise: On your quiz, circle the right choice in every row and write all 5 letters in the answer box.
Problem 9
3 pointsPower of a productWrite as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 145·55=
(4·5)5 Power of a product, read backwards: two powers with the same exponent multiply into one power of the product of the bases.
- Step 2=
205 4·5=
20 , and the shared exponent 5 stays 5.
Answer
Written as: a single power
The trap
A common wrong answer: 95
95 adds the bases (4+
Write as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 135·55=
(3·5)5 Power of a product, read backwards: two powers with the same exponent multiply into one power of the product of the bases.
- Step 2=
155 3·5=
15 , and the shared exponent 5 stays 5.
Answer
Written as: a single power
The trap
A common wrong answer: 85
85 adds the bases (3+
Watch it explained
Exponent properties 5 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a product exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Problem 10
8 pointsPower of a quotient · power of a powerCircle one choice in each row. Write your final choices in the answer box.
For p3, I can … the … because …; for the denominator 2, I can …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
For p3, I can (b) multiply
Power of a power: p3 raised to the power 4 means multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base p stays p.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because p3 is inside the parentheses and 4 is the power outside them.
- Step 4
For the denominator 2, I can (c) raise it to the power 4
Power of a quotient: the power 4 goes on the top and on the bottom, so the denominator 2 is raised to the power 4 too.
- Step 5
so the answer is (d) p1216
(p32)4=p3·424= p1216 Power of a quotient with a power of a power: 3·4=
12 on top and 24=16 on the bottom, so choice (d).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (a) p12/2
Choice (a) raises only the top, but the power of a quotient raises the bottom too: 24=
Circle one choice in each row. Write your final choices in the answer box.
For x2, I can … the … because …; for the denominator 3, I can …, so the answer is …
Try it first on paper. Then check one step at a time.
- Step 1
For x2, I can (b) multiply
Power of a power: x2 raised to the power 3 means multiply the exponents.
- Step 2
the (b) exponents
Power of a power: only the exponents change; the base x stays x.
- Step 3
because (d) I am raising a power inside the parentheses to another power outside the parentheses
The power of a power applies because x2 is inside the parentheses and 3 is the power outside them.
- Step 4
For the denominator 3, I can (c) raise it to the power 3
Power of a quotient: the power 3 goes on the top and on the bottom, so the denominator 3 is raised to the power 3 too.
- Step 5
so the answer is (a) x627
(x23)3=x2·333= x627 Power of a quotient with a power of a power: 2·3=
6 on top and 33=27 on the bottom, so choice (a).
Answer
Written as: one choice in each row, then the answer
The trap
A common wrong answer: (b) x6/3
Choice (b) raises only the top, but the power of a quotient raises the bottom too: 33=
Watch it explained
Exponent properties 6 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a quotient exponents"
Now revise: On your quiz, circle the right choice in every row and write all 5 letters in the answer box.
Now revise: On your quiz, circle the right choice in every row and write all 5 letters in the answer box.
Problem 11
3 pointsPower of a quotientWrite as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 114323=
(142)3 Power of a quotient, read backwards: the top and the bottom have the same exponent, so it is one power of the quotient of the bases.
- Step 2=
73 14÷2=
7 , and the shared exponent 3 stays 3.
Answer
Written as: a single power
The trap
A common wrong answer: 123
123 subtracts the bases (14−
Write as a single power. Show your work.
Try it first on paper. Then check one step at a time.
- Step 120343=
(204)3 Power of a quotient, read backwards: the top and the bottom have the same exponent, so it is one power of the quotient of the bases.
- Step 2=
53 20÷4=
5 , and the shared exponent 3 stays 3.
Answer
Written as: a single power
The trap
A common wrong answer: 163
163 subtracts the bases (20−
Watch it explained
Exponent properties 6 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a quotient exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power.
Problem 12
3 pointsZero exponentEvaluate. Assume t≠
Try it first on paper. Then check one step at a time.
- Step 15t0=
5·1= 5 Zero exponent: only the t is raised to the power 0, so t0=
1 and the 5 stays. - Step 2(5t)0=
1 Zero exponent: the whole product 5t is inside the parentheses, so all of it equals 1.
- Step 35t0+
(5t)0= 5+ 1= 6 Add the two values: 5+
1= .6
Answer
Written as: a whole number
The trap
A common wrong answer: 2
2 turns 5t0 into 1, but the zero exponent applies only to the t: 5t0=
Evaluate. Assume p≠
Try it first on paper. Then check one step at a time.
- Step 17p0=
7·1= 7 Zero exponent: only the p is raised to the power 0, so p0=
1 and the 7 stays. - Step 2(7p)0=
1 Zero exponent: the whole product 7p is inside the parentheses, so all of it equals 1.
- Step 37p0+
(7p)0= 7+ 1= 8 Add the two values: 7+
1= .8
Answer
Written as: a whole number
The trap
A common wrong answer: 2
2 turns 7p0 into 1, but the zero exponent applies only to the p: 7p0=
Watch it explained
The zeroth power | Arithmetic operations | 6th grade | Khan Academy
Video by Khan Academy
Open on YouTube · Khan Academy lesson page
If the video will not play, search Google for: "Khan Academy zero exponent"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a whole number.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a whole number.
Problem 13
5 pointsPower of a power · quotient of powersWrite as a single power. Assume x≠
Try it first on paper. Then check one step at a time.
- Step 1(x2)5x4=
x10x4 Power of a power first: multiply the exponents, 2·5=
10 . - Step 2=
x10−4 Quotient of powers: same base, dividing, so subtract the exponents, top minus bottom.
- Step 3=
x6 10−
4= : a single power with a positive exponent.6
Answer
Written as: a single power with a positive exponent
The trap
A common wrong answer: x3
x3 adds the exponents in the power (2+
Write as a single power. Assume y≠
Try it first on paper. Then check one step at a time.
- Step 1(y3)4y5=
y12y5 Power of a power first: multiply the exponents, 3·4=
12 . - Step 2=
y12−5 Quotient of powers: same base, dividing, so subtract the exponents, top minus bottom.
- Step 3=
y7 12−
5= : a single power with a positive exponent.7
Answer
Written as: a single power with a positive exponent
The trap
A common wrong answer: y2
y2 adds the exponents in the power (3+
Watch it explained
Exponent properties 3 | Exponent expressions and equations | Algebra I | Khan Academy
Video by Khan Academy
If the video will not play, search Google for: "Khan Academy power of a power exponents"
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power with a positive exponent.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a single power with a positive exponent.
Problem 14
6 pointsProduct of powers · quotient of powers · negative exponentEvaluate. Write as a decimal. Show your work.
Try it first on paper. Then check one step at a time.
- Step 123·2429=
2729 Product of powers on top: same base, multiplying, so add the exponents: 3+
4= .7 - Step 2=
27−9= 2−2 Quotient of powers: subtract the bottom exponent from the top one: 7−
9= .−2 - Step 3=
122= 14 Negative exponent: 2−2 is the reciprocal 122, a positive number, and 22=
4 . - Step 4=
0.25 Write the fraction as the decimal the item asks for: 1÷4=
0.25 .
Answer
Written as: a decimal
The trap
A common wrong answer: 4
4 comes from subtracting backwards (9−
Evaluate. Write as a decimal. Show your work.
Try it first on paper. Then check one step at a time.
- Step 152·5559=
5759 Product of powers on top: same base, multiplying, so add the exponents: 2+
5= .7 - Step 2=
57−9= 5−2 Quotient of powers: subtract the bottom exponent from the top one: 7−
9= .−2 - Step 3=
152= 125 Negative exponent: 5−2 is the reciprocal 152, a positive number, and 52=
25 . - Step 4=
0.04 Write the fraction as the decimal the item asks for: 1÷25=
0.04 .
Answer
Written as: a decimal
The trap
A common wrong answer: 25
25 comes from subtracting backwards (9−
Watch it explained
Negative exponents | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy
Video by Khan Academy
Open on YouTube · Khan Academy lesson page
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Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a decimal.
Now revise: On your quiz, redo the problem with every step written and the law named, then box your answer as a decimal.