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Exponents and Roots Practice

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Exponents and Roots Practice

Simplify each expression or solve each problem. Show your work where space is provided. Assume variables are nonzero when using quotient or zero-exponent rules.

Multiple Choice

Choose the best answer for each expression or problem.

1.What is the value of 4³?

2.Simplify 3⁴ × 3².

3⁶ = 729
3⁸ = 6,561
9⁶ = 531,441
3² = 9

3.Evaluate √196.

4.For a nonzero number a, what is a⁰ equal to?

0
1
a
−1

5.Round √70 to the nearest whole number. Use the number line to help you locate it between consecutive integers.

6.Simplify (2³)⁴.

2⁷ = 128
2¹² = 4,096
2⁸ = 256
8⁵ = 32,768

Work It Out

Write enough steps to make your reasoning clear.

7.Evaluate 3⁴ − √121 + 2⁰.

8.Simplify 8⁷ ÷ 8³. State the exponent rule you used and give the value of the simplified expression.

9.A square patio has an area of 289 square feet. Find the length of one side, showing how a square root gives your result.

10.A model uses the formula V = s²h. If s = 5 centimeters and h = 3 centimeters, calculate V.

11.Simplify (x⁵)³ ÷ x⁴, assuming x ≠ 0. Show the exponent laws you apply.

12.A square display has an area of 400 square inches. What is its perimeter? Find the side length first.

Match Each Rule

Match each expression to the exponent rule it demonstrates. Each rule is used once.

13.Match each expression with the correct rule.

m⁴ × m⁶
(p³)²
r⁹ ÷ r⁵
q⁰, where q ≠ 0

C. Product rule
D. Power-of-a-power rule
B. Quotient rule
A. Zero exponent rule

Product rule: aᵐ · aⁿ = aᵐ⁺ⁿ | Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0) Power of a power: (aᵐ)ⁿ = aᵐⁿ | Zero exponent: a⁰ = 1 (a ≠ 0) Square root: √n is the nonnegative number whose square is n. Perfect squares to remember include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 289, and 400.