8th Grade Math · Exponent Rules
Power of a power Worksheets
Fresh practice, ready to print. Answer key included.
Problems such as (3²)⁴ = 3⁸.
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Or start with a ready-made version.
How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| To do this | Use this rule |
|---|---|
| Multiply powers, same base | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Divide powers, same base | aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ |
| Zero exponent | a⁰ = 1 |
| Negative exponent | a⁻ⁿ = 1/aⁿ |
Worked example
Find 3² × 3⁻⁵.
- 1The bases are the same, so add the exponents: 2 + (−5) = −3. The product is 3⁻³.
- 2A negative exponent means one over the power: 3⁻³ = 1/3³.
- 33³ = 27, so the answer is 1/27.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Power of a power Worksheets, version 1Worksheet PDFAnswer key PDF
- Power of a power Worksheets, version 2Worksheet PDFAnswer key PDF
- Power of a power Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (expressions and equations) and aligned to CCSS 8.EE.A.1. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet code printed at the bottom of each page pairs a sheet with its key.
- Why do the first sections ask for a single power instead of a number?
- Writing 2³ × 2⁴ as 2⁷ is the rule itself, and it keeps the arithmetic small. The last two sections ask for a number once the rules are familiar.
- Does a negative exponent make the answer negative?
- No. 2⁻³ is 1/8, not −8. The negative exponent means one over the power. This is the most common mistake, so the zero and negative section practises it on its own.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.
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