Year 8 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 8 indices & scientific notation worksheet.

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Year 8 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Use the index laws. Write answers with positive indices.

1.Write 2⁻² as a fraction.

Answer:

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

2.Simplify: (x⁴)⁵

Answer: x²⁰

Multiply the indices: 4 × 5 = 20

3.Evaluate: 5⁰

Answer: 1

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

4.Simplify: 6x⁴ × 3x⁵

Answer: 18x⁹

6 × 3 = 18; add the indices: 9

5.Simplify: 3x⁴ × 4x⁸

Answer: 12x¹²

3 × 4 = 12; add the indices: 12

6.Simplify: 6x² × 2x⁴

Answer: 12x⁶

6 × 2 = 12; add the indices: 6

7.Simplify: (x³)³

Answer: x⁹

Multiply the indices: 3 × 3 = 9

8.Write 2⁻³ as a fraction.

Answer:

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

9.Evaluate: 7⁰

Answer: 1

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

10.Simplify: (x⁵)⁸

Answer: x⁴⁰

Multiply the indices: 5 × 8 = 40

11.Simplify: 3x³ × 2x⁹

Answer: 6x¹²

3 × 2 = 6; add the indices: 12

12.Simplify: (x⁴)⁹

Answer: x³⁶

Multiply the indices: 4 × 9 = 36

13.Write 3⁻² as a fraction.

Answer:

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

14.Simplify: 6x⁶ × 4x⁷

Answer: 24x¹³

6 × 4 = 24; add the indices: 13

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