9th Grade Laws of Exponents Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 9th Grade exponents & scientific notation worksheet.

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9th Grade Laws of Exponents Worksheet — Level 3 — Answers

Use the laws of exponents. Write answers with positive exponents.

1.Write 5⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 5² = 1 ÷ 25

2.Simplify: (x⁴)²

Answer: x⁸

Multiply the exponents: 4 × 2 = 8

3.Simplify: (x⁸)⁸

Answer: x⁶⁴

Multiply the exponents: 8 × 8 = 64

4.Simplify: (x⁶)⁶

Answer: x³⁶

Multiply the exponents: 6 × 6 = 36

5.Write 10⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 10¹ = 1 ÷ 10

6.Evaluate: 4⁰

Answer: 1

Anything (except 0) to the power of 0 equals 1.

7.Evaluate: 5⁰

Answer: 1

Anything (except 0) to the power of 0 equals 1.

8.Simplify: (x⁷)⁴

Answer: x²⁸

Multiply the exponents: 7 × 4 = 28

9.Evaluate: 7⁰

Answer: 1

Anything (except 0) to the power of 0 equals 1.

10.Simplify: (x⁴)³

Answer: x¹²

Multiply the exponents: 4 × 3 = 12

11.Write 5⁻³ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 5³ = 1 ÷ 125

12.Write 3⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 3¹ = 1 ÷ 3

13.Simplify: 3x⁴ × 3x⁶

Answer: 9x¹⁰

3 × 3 = 9; add the exponents: 10

14.Write 2⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2¹ = 1 ÷ 2

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