Wayground
Product and Quotient of Powers - Printable Math Worksheets 8th - 10th Grade - Wayground

Product and Quotient of Powers

Abi Carlson

Created by Abi Carlson

10 questions

8th - 10th Grade

Math

Updated Oct 2026

Product and Quotient of Powers is a free printable mathematics worksheet for students in Grades 8–10. It contains 10 multiple-choice questions that ask students to simplify expressions involving products and quotients of powers, including expressions with numerical and variable factors. The answer choices require students to apply exponent rules accurately and distinguish between similar-looking simplified forms. Use this worksheet to reinforce procedural fluency with multiplying and dividing powers and to check whether students can track bases, coefficients, and exponents while simplifying. Students select an answer for each expression, making the worksheet useful for guided practice, independent work, homework, or a quick formative assessment after instruction. A complete answer key is included, and the worksheet is available as a free printable PDF for classroom use.

Worksheet settings

Font size

S
M
L
XL
WaygroundWorksheets

Product and Quotient of Powers

Total questions: 10

Name
Class
Date
1.

Simplify:

t9⋅t8t^9\cdot t^8  

a)

t1t^1  

b)

t72t^{72}  

c)

  t17t^{17}  

d)

None of the above

2.

Simplify:

78⋅77^8\cdot7  

a)

  797^9  

b)

  49849^8  

c)

787^8  

d)

None of the above

3.

Simplify:

(6x2)(−3x5)\left(6x^2\right)\left(-3x^5\right)  

a)

  18x718x^7  

b)

  −18x7-18x^7  

c)

3x73x^7  

d)

None of the above

4.

Simplify:

c5⋅c3⋅c3c^5\cdot c^3\cdot c^3  

a)

  c45c^{45}  

b)

  3c113c^{11}  

c)

  c11c^{11}  

d)

None of the above

5.

Simplify:


10u3v5⋅7v310u^3v^5\cdot7v^3  

a)

  70u3v1570u^3v^{15}  

b)

  17u3v817u^3v^8  

c)

  70u3v870u^3v^8  

d)

None of the above

6.

Simplify:

9792\frac{9^7}{9^2}  

a)
95
b)
99
c)
15
d)
9-5
7.

Simplify:

62664\frac{6^{26}}{6^4}  

a)
122
b)
130
c)
622
d)
630
8.

Simplify:

28z1026z3\frac{2^8z^{10}}{2^6z^3}  

a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
9.

Simplify:

x3yxy5\frac{x^3y}{xy^5}   

a)

x2y−4x^2y^{-4}  

b)

y4x2\frac{y^4}{x^2}  

c)

x4y2\frac{x^4}{y^2}  

d)

x2y4x^2y^4  

10.

Simplify:

45x6y95x4y2\frac{45x^6y^9}{5x^4y^2}  

a)

9x2y7\frac{9}{x^2y^7}  

b)

1x2y7\frac{1}{x^2y^7}  

c)

x2y7x^2y^7  

d)

9x2y79x^2y^7  

WaygroundAnswer Key

Product and Quotient of Powers

Total questions: 10

1.
c)

  t17t^{17}  

2.
a)

  797^9  

3.
b)

  −18x7-18x^7  

4.
c)

  c11c^{11}  

5.
c)

  70u3v870u^3v^8  

6.
a) 95
7.
c) 622
8.
d) 22 z7
9.
a)

x2y−4x^2y^{-4}  

10.
d)

9x2y79x^2y^7  

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Product and Quotient of Powers worksheet cover?

This Grade 8–10 mathematics worksheet provides 10 multiple-choice questions on simplifying products and quotients of powers. Students must apply exponent rules to expressions with numerical and variable factors, then identify the correctly simplified form from several choices.

How can I use this worksheet to teach simplifying products and quotients of powers?

First model how to simplify one product of powers and one quotient of powers, explicitly tracking which factors share a base and how their exponents change. Then have students solve the worksheet items independently and explain why their selected option represents the simplified expression, especially when distractors differ only in an exponent or coefficient.

What mistakes should I watch for when students simplify these powers?

Watch for students choosing a distractor because they combine exponents incorrectly, use the product rule on a quotient, or change a coefficient when only the exponent operation should change. The multiple-choice format can also reveal whether students are confusing numerical factors with variable bases or failing to preserve the correct base while simplifying.

How do I assign and grade this Product and Quotient of Powers worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printed submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz.

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 numerical and variable expressions are easier to read. You can also apply a dyslexia-friendly font or translate the simplifying-powers worksheet into another language when appropriate.

Where can I find more worksheets like this on Wayground?

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

© 2026 Wayground Inc.

Accessibility and Inclusion