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Exponents and Roots Practice

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Exponents and Roots Practice

Help a game-design team check its calculations. Simplify exponent expressions, find roots, and explain your reasoning. Show work where space is provided.

Exponent Rules in Action

Use the exponent rules. Remember: when multiplying powers with the same base, add the exponents; when dividing, subtract them; and a power raised to a power means multiply the exponents.

1.A game character earns 3⁴ points in one round and 3² points in another. Simplify 3⁴ × 3² as a single power, then evaluate it.

2.A computer divides 5⁶ data packets equally into groups of 5⁴. Simplify 5⁶ ÷ 5⁴ as a single power, then evaluate.

3.A square tile has side length 2³ inches. Its area is (2³)² square inches. Simplify the expression as a single power and evaluate.

4.A code uses 10⁰ as its starting multiplier. What number does 10⁰ equal?

5.A tiny sensor reading is 10⁻². Write this value as a fraction and as a decimal.

Roots and Number Sense

A root reverses a power: √49 asks which positive number squared equals 49. Use the number line to help compare powers of 2.

6.On the number line, the marked values are 2⁻², 2⁰, and 2³. Match each value to the correct point, then write the values from least to greatest.

7.Find the positive square root: √49 = .

8.A cube-shaped prize has a volume of 216 cubic inches. What is the length of one edge? Use the fact that the volume is side³.

9.Evaluate both roots: √81 and ∛125.

Final Challenge

Combine exponent rules and explain what the equation tells you.

10.A game effect is calculated as (2⁵ × 2⁻³) ÷ 2². Simplify it as a single power of 2, then evaluate.

11.True or false? If x² = 64, then x must be 8. Explain why the equation may have more than one solution.

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About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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