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Exponent Laws Practice

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Exponent Laws Practice

Simplify each expression using exponent laws. Assume variables are nonzero whenever they appear in a denominator or have a negative exponent. Show your steps for the written problems.

Spot the Rule

Choose the best answer for each expression.

1.A robot combines matching powers: x⁵ · x³. Which expression is equivalent?
  • x⁸
  • x¹⁵
  • x²
  • 2x⁸
2.A game displays (3²)⁴ as one power of 3. What should it display?
  • 3⁶
  • 3⁸
  • 3¹⁶
  • 3²
3.A sensor simplifies y⁸ ÷ y³. What is the result?
  • y⁵
  • y¹¹
  • y²⁴
  • y⁻⁵
4.A mystery code asks for the value of 7⁰. What number unlocks it?
  • 0
  • 1
  • 7
  • 70

Build and Simplify

Write each answer in simplest form. Include enough working to show which exponent law you used.

5.A game level combines three matching powers: a⁴ · a⁶ · a². Simplify the expression.
6.A square-based power appears in a program as (2x³)⁴. Simplify completely.
7.A machine divides m¹⁰ by m⁴. Simplify the result.
8.Rewrite x⁻⁵ using only positive exponents.

Final Challenges

Use the exponent laws to solve each challenge. Take care with negative exponents and explanations.

9.A formula for a tiny rocket part is (3x²y⁻¹)³ ÷ (x⁴y²). Simplify completely and write the answer with positive exponents.
10.A code has the form 2ˣ = 32. Find x.
11.A teammate claims x³ · x⁵ = x¹⁵. Is the claim true or false? Correct it and explain the rule for multiplying powers with the same base.

2 printable pages

  • Exponent Laws Practice, page 1 of 2: Spot the Rule, Build and Simplify

    Page 1

  • Exponent Laws Practice, page 2 of 2: Final Challenges

    Page 2

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