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Integer Exponents: Practice and Answer Key

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Integer Exponents: Practice and Answer Key

Simplify each expression. Write answers with positive exponents unless a question says otherwise. Answers are included so you can check your work. Assume variables are nonzero when they appear in denominators.

Exponent rules

Use these rules as you work: multiply like bases → add exponents; divide like bases → subtract exponents; power of a power → multiply exponents; a⁰ = 1 for a ≠ 0; a⁻ⁿ = 1/aⁿ.

1.A game score is recorded as 3⁴ × 3². Simplify the expression and evaluate it.
2.A storage system reduces 5⁷ units by a factor of 5³. Simplify 5⁷ ÷ 5³ and evaluate.
3.Which expression is equivalent to (2³)⁴? Choose one.
  • 2⁷
  • 2¹²
  • 2⁸
  • 6⁴
4.Evaluate 4⁰. Explain why the answer is not zero.
5.Rewrite 6⁻³ using only positive exponents, then evaluate.

Variables and applications

Keep coefficients and variable factors organized. A negative exponent means reciprocal; it does not make the value negative.

6.A model scales a measurement by (3x²)³. Simplify fully.
7.Simplify 8x⁵y⁻² ÷ 2x²y³. Write the result using positive exponents.
8.A student rewrites (2a⁻³b²)⁻² as 4a⁶b⁻⁴. Find and correct the coefficient error, then give the expression with positive exponents.
9.Solve 2ˣ = 32. Show how you identify the exponent.
10.Simplify (x⁻²y³)⁻¹ × (xy⁻¹)². Write the result using positive exponents.
11.A power-of-three code is 3ˣ⁺² = 81. Find x.
12.A tiny measurement is written as (4 × 10³)(2 × 10⁻⁵). Express the product in scientific notation.

3 printable pages

  • Integer Exponents: Practice and Answer Key, page 1 of 3: Exponent rules

    Page 1

  • Integer Exponents: Practice and Answer Key, page 2 of 3: Variables and applications

    Page 2

  • Integer Exponents: Practice and Answer Key, page 3 of 3: 12. A tiny measurement is written as (4 × 10³)(2 × 10⁻⁵). Express the product in…

    Page 3

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