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

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

1.Simplify: (x⁷)⁷

Answer: x⁴⁹

Multiply the exponents: 7 × 7 = 49

2.Simplify: 5x⁸ × 5x²

Answer: 25x¹⁰

5 × 5 = 25; add the exponents: 10

3.Write 2⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2² = 1 ÷ 4

4.Simplify: 5x⁷ × 5x⁴

Answer: 25x¹¹

5 × 5 = 25; add the exponents: 11

5.Simplify: 2x⁷ × 2x⁷

Answer: 4x¹⁴

2 × 2 = 4; add the exponents: 14

6.Evaluate: 2⁰

Answer: 1

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

7.Evaluate: 9⁰

Answer: 1

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

8.Simplify: 6x⁷ × 5x⁹

Answer: 30x¹⁶

6 × 5 = 30; add the exponents: 16

9.Simplify: 6x⁸ × 2x⁴

Answer: 12x¹²

6 × 2 = 12; add the exponents: 12

10.Write 2⁻³ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2³ = 1 ÷ 8

11.Simplify: 4x⁸ × 4x⁵

Answer: 16x¹³

4 × 4 = 16; add the exponents: 13

12.Write 10⁻¹ as a fraction.

Answer:

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

13.Simplify: 6x⁹ × 3x³

Answer: 18x¹²

6 × 3 = 18; add the exponents: 12

14.Write 3⁻³ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 3³ = 1 ÷ 27

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