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Worksheets›Grade 8›Exponents & roots›Laws of exponents

Laws of Exponents Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Grade 8CCSS 8.EE.A.1Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Product and quotient rules

  1. 1.a6 · a5
  2. 2.a6 · a6
  3. 3.a5 · a5
  4. 4.m5 · m2
  5. 5.x2 · x7
  6. 6.y2 · y9
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Multiply powers with the same base by adding exponents, divide by subtracting, and raise a power to a power by multiplying.

Easym7 · m5Product and quotient rulesMedium(m6)4Power rules with coefficientsHard5455 =Zero and negative exponents

How to solve it: a worked example

Simplify. Write answers with positive exponents.

  1. Starty8 · y8
  2. Add the exponents: 8 + 8 = 16y16
  3. Answery16

Common mistakes to watch for

  • Multiplying the exponents in a product instead of adding them.
  • Forgetting to raise the coefficient: (2x³)² = 4x⁶, not 2x⁶.
  • Reading a negative exponent as a negative number: 2⁻³ = 1/8, not −8.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Scientific notationSquare roots & cube rootsMulti-step equationsEquations with variables on both sidesSystems of equations

FAQ

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix laws of exponents with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.