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Quotient of Powers Property - Printable Math Worksheets 7th Grade - Wayground

Quotient of Powers Property

Ariana Wanderlingh

Created by Ariana Wanderlingh

20 questions

7th Grade

Math

Updated Oct 2026

Quotient of Powers Property is a Grade 7 mathematics worksheet that helps students simplify expressions involving powers with the same base. Across 20 multiple-choice questions, students apply the quotient rule by keeping the base and subtracting the exponents, including numerical expressions such as 15⁹ ÷ 15³ and expressions that include variables. Several items ask students to write simplified answers as powers, while others use true-or-false and rule-identification formats. This free printable worksheet with an answer key supports guided practice, independent review, or a quick check of students’ understanding of the division law for exponents. Its answer choices include common errors such as adding exponents, changing the base, or using an incorrect negative or fractional form, giving teachers useful insight into students’ reasoning. It is designed for Grade 7 math instruction on simplifying quotients of powers.

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Quotient of Powers Property

Total questions: 20

Name
Class
Date
1.
159÷153 =
a)
156
b)
1512
c)
16
d)
112
2.
Question Image
a)
a8b13
b)
a2b7
c)
a15b30
3.
Evaluate this expression using the quotient rule.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
4.
Evaluate the expression using the quotient rule.
Evaluate the expression using the quotient rule.
a)
122
b)
130
c)
622
d)
630
5.
Evaluate the expression using the quotient rule.
Evaluate the expression using the quotient rule.
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
6.
True or False:
True or False: 
a)
True 
b)
False
7.
Simplify the expression.
Simplify the expression.
a)
76
b)
7-5
c)
1/75
d)
75
8.

Simplify the expression. Write your answer as a power.

9892\frac{9^8}{9^2}  

a)

949^4  

b)

969^6  

c)

9109^{10}  

d)

9169^{16}  

9.

Simplify the expression. Write your answer as a power.

h10h3\frac{h^{10}}{h^3}  

a)

h7h^7  

b)

h13h^{13}  

c)

h103h^{\frac{10}{3}}  

d)

h30h^{30}  

10.

Simplify the expression. Write your answer as a power.

(−2)9(−2)4\frac{\left(-2\right)^9}{\left(-2\right)^4}  

a)

−25-2^5  

b)

(−2)13\left(-2\right)^{13}  

c)

(−2)36\left(-2\right)^{36}  

d)

(−2)5\left(-2\right)^5  

11.

Simplify the expression. Write your answer as a power.

(1.5)12(1.5)2\frac{\left(1.5\right)^{12}}{\left(1.5\right)^2}  

a)

(1.5)6\left(1.5\right)^6  

b)

(1.5)4\left(1.5\right)^4  

c)

(1.5)14\left(1.5\right)^{14}  

d)

(1.5)10\left(1.5\right)^{10}  

12.

Simplify the expression. Write your answer as a power.

(−5)4(−5)\frac{\left(-5\right)^4}{\left(-5\right)}  

a)

−54-5^4  

b)

(−5)3\left(-5\right)^3  

c)

(−5)5\left(-5\right)^5  

d)

(−5)4\left(-5\right)^4  

13.

Simplify the expression. Write your answer as a power.

a3a⋅a5a3\frac{a^3}{a}\cdot\frac{a^5}{a^3}  

a)

a4a^4  

b)

a8a^8  

c)

a5a^5  

d)

a2a^2  

14.

Simplify the expression. Write your answer as a power.

b7⋅b⋅b5b10\frac{b^7\cdot b\cdot b^5}{b^{10}}  

a)

b2b^2  

b)

b23b^{23}  

c)

b13b^{13}  

d)

b3b^3  

15.

Simplify the expression. Write your answer as a power.

c14⋅c8c\frac{c^{14}\cdot c^8}{c}  

a)

c20c^{20}  

b)

c21c^{21}  

c)

c22c^{22}  

d)

c4c^4  

16.
Division Law states: keep the base the same and do this to the exponents.
a)
multiply
b)
add
c)
subtract
d)
divide
17.

Simplify and write with positive exponents only.

x10x2\frac{x^{10}}{x^2}  

a)

x18x^{18}  

b)

x8x^8  

c)

x20x^{20}  

d)

x12x^{12}  

18.

Which expression is an example of the "Quotient of Powers Property?"

a)

3x2⋅2y03x^2\cdot2y^0  

b)

2x93x15\frac{2x^9}{3x^{15}}  

c)

(3x2y)4\left(3x^2y\right)^4  

d)

3x2y−43x^2y^{-4}  

19.
Simplify the expression.
Simplify the expression.
a)
76
b)
7-5
c)
1/75
d)
75
20.

When using the "Quotient of Powers" rule, you can only subtract when the ____________ are the same.

a)

cookies

b)

ages

c)

exponents

d)

bases

WaygroundAnswer Key

Quotient of Powers Property

Total questions: 20

1.
a) 156
2.
b) a2b7
3.
a) 95
4.
c) 622
5.
d) 22 z7
6.
a) True 
7.
d) 75
8.
b)

969^6  

9.
a)

h7h^7  

10.
d)

(−2)5\left(-2\right)^5  

11.
d)

(1.5)10\left(1.5\right)^{10}  

12.
b)

(−5)3\left(-5\right)^3  

13.
a)

a4a^4  

14.
d)

b3b^3  

15.
b)

c21c^{21}  

16.
c) subtract
17.
b)

x8x^8  

18.
b)

2x93x15\frac{2x^9}{3x^{15}}  

19.
d) 75
20.
d)

bases

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FAQs

What does the Quotient of Powers Property worksheet cover?

This Grade 7 worksheet uses 20 multiple-choice items to practise simplifying quotients of powers with the same base. Students keep the base, subtract the exponents, and express results as powers, including examples with numerical bases and variable-containing expressions, along with true-or-false and division-law questions.

How can I use this worksheet to teach the quotient rule for exponents?

Begin by modeling one same-base division expression and explicitly showing that the base stays the same while the exponents are subtracted. Then use the worksheet’s numerical and variable-containing multiple-choice items to have students explain why each answer choice is correct or incorrect, ending with the division-law question as a verbal check of the rule.

What mistakes should I watch for when students complete this worksheet?

Watch for students who add, multiply, or divide the exponents instead of subtracting them, or who change the base while simplifying. The answer choices also reveal errors such as reversing the exponent subtraction, writing a reciprocal or negative-exponent form unnecessarily, and failing to write the final result as a single power.

How do I assign and grade the Quotient of Powers Property worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground, and it includes a complete answer key for all 20 multiple-choice questions. For printable submissions, scan student work with the Wayground for Teachers app to support grading and review.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the exponent expressions and multiple-choice options are easier to read. You can also enable a dyslexia-friendly font or translate the quotient-of-powers questions into another language when that better supports access to the practice.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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