Year 9 Index Laws Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the Year 9 indices & scientific notation worksheet.

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Year 9 Index Laws Worksheet — Level 3 — Practice Set 2 — Answers

Use the index laws. Write answers with positive indices.

1.Evaluate: 6⁰

Answer: 1

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

2.Simplify: 3x⁵ × 2x⁴

Answer: 6x⁹

3 × 2 = 6; add the indices: 9

3.Simplify: 2x⁷ × 2x⁷

Answer: 4x¹⁴

2 × 2 = 4; add the indices: 14

4.Evaluate: 7⁰

Answer: 1

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

5.Write 10⁻¹ as a fraction.

Answer:

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

6.Simplify: 3x⁵ × 5x²

Answer: 15x⁷

3 × 5 = 15; add the indices: 7

7.Simplify: (x⁹)³

Answer: x²⁷

Multiply the indices: 9 × 3 = 27

8.Write 3⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 3² = 1 ÷ 9

9.Write 2⁻² as a fraction.

Answer:

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

10.Simplify: 5x⁶ × 5x⁴

Answer: 25x¹⁰

5 × 5 = 25; add the indices: 10

11.Write 2⁻³ as a fraction.

Answer:

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

12.Simplify: (x⁴)⁷

Answer: x²⁸

Multiply the indices: 4 × 7 = 28

13.Simplify: (x⁵)³

Answer: x¹⁵

Multiply the indices: 5 × 3 = 15

14.Simplify: (x⁹)⁸

Answer: x⁷²

Multiply the indices: 9 × 8 = 72

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