Year 9 Index Laws Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: 4x² × 2x⁶

Answer: 8x⁸

4 × 2 = 8; add the indices: 8

2.Write 10⁻³ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 10³ = 1 ÷ 1000

3.Simplify: (x⁴)⁹

Answer: x³⁶

Multiply the indices: 4 × 9 = 36

4.Write 3⁻³ as a fraction.

Answer:

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

5.Evaluate: 6⁰

Answer: 1

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

6.Write 10⁻¹ as a fraction.

Answer:

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

7.Write 5⁻³ as a fraction.

Answer:

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

8.Evaluate: 9⁰

Answer: 1

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

9.Simplify: (x⁴)⁷

Answer: x²⁸

Multiply the indices: 4 × 7 = 28

10.Evaluate: 5⁰

Answer: 1

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

11.Simplify: 6x⁶ × 5x⁴

Answer: 30x¹⁰

6 × 5 = 30; add the indices: 10

12.Simplify: 4x⁴ × 4x⁹

Answer: 16x¹³

4 × 4 = 16; add the indices: 13

13.Simplify: 6x² × 4x⁵

Answer: 24x⁷

6 × 4 = 24; add the indices: 7

14.Simplify: (x³)⁹

Answer: x²⁷

Multiply the indices: 3 × 9 = 27

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