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Exponents - Product Rule - Printable Mathematics Worksheets - Wayground

Exponents - Product Rule

12 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet provides 12 multiple-choice questions on identifying the base and exponent, converting between exponential and expanded forms, and applying the product rule for powers with the same base. Students interpret expressions such as 3⁴, represent repeated multiplication as a power, identify correct exponent vocabulary, and simplify products such as 2² × 2³ and x²⁰ × x¹⁰ by adding exponents. Use this free printable worksheet to check whether students can connect exponent notation to repeated multiplication and apply the same-base product rule accurately. It works well for independent practice, a short review, or a formative assessment after direct instruction. The worksheet includes a complete answer key, making it straightforward to identify whether errors come from reading the base and exponent, expanding a power, or applying the exponent rule.

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Worksheets

Exponents - Product Rule

Total questions: 12

Name
Class
Date
1.

Which number is the BASE?

23 = 8

a)

2

b)

8

c)

3

d)

238

2.

Which number is the EXPONENT?

42 = 16

a)

4

b)

16

c)

2

d)

162

3.

52 , in this example, 5 is the ______ and 2 is the _______

a)

base, product

b)

exponent, base

c)

base, exponent

d)

product, base

4.

Write the product as a power :

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-25

b)

2-5

c)

(-2)5

d)

(-2)-5

5.

Which expression is in expanded form?

a)

53

b)

5x5x5

c)

125

d)

53

6.

Which expression is equivalent to 34?

a)

3+3+3+3

b)

4+4+4

c)

4x4x4

d)

3x3x3x3

7.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

8.

22 x 23

a)

46

b)

45

c)

26

d)

25

9.

x20 . x10

a)

x30

b)

x200

c)

2x30

d)

x10

10.

If the bases are the same, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

11.

2 * 22 *22

a)

24

b)

84

c)

36

d)

25

12.

How do you correctly say 43

a)

4 squared

b)

3 quadrupled

c)

4 cubed

d)

4 to the power of 2

Answer Key

Exponents - Product Rule

Total questions: 12

1.
a)

2

2.
c)

2

3.
c)

base, exponent

4.
c)

(-2)5

5.
b)

5x5x5

6.
d)

3x3x3x3

7.
b)

Add

8.
d)

25

9.
a)

x30

10.
c)

Add the exponents

11.
d)

25

12.
c)

4 cubed

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FAQs

What does the Exponents - Product Rule worksheet cover?

This Grade 8 worksheet uses 12 multiple-choice questions to practice identifying bases and exponents, translating between powers and expanded multiplication, and applying the product rule when multiplying powers with the same base. Students must recognize that the base stays the same while the exponents are added, as in 2² × 2³ = 2⁵ and x²⁰ × x¹⁰ = x³⁰.

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

Begin by reviewing the base, exponent, and expanded form items so students connect notation such as 3⁴ with 3 × 3 × 3 × 3. Then use the product-rule questions to have students explain why multiplying equal bases combines the repeated factors and leads to adding exponents. Ask students to justify an answer such as 2² × 2³ = 2⁵ by writing out the five factors of 2.

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

Watch for students reversing the base and exponent, treating an expanded expression such as 5 × 5 × 5 as a power without identifying its exponent, or choosing to multiply the exponents instead of adding them. Students may also mishandle the negative base in (-2)⁵ or confuse the wording for 4³, which is “4 cubed.”

How do I assign and grade this Exponents - Product Rule worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the 12 multiple-choice questions. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade responses efficiently.

How can I differentiate this exponents worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing between the exponent examples and answer choices, or increase the font size for clearer reading of superscripts and symbols. You can also select a dyslexia-friendly font or translate the worksheet into another language when those options better support access to the multiple-choice items.

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.

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