Year 8 Index Laws Worksheet — Level 3 — Practice Set 2 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Indices & Scientific Notation

Year 8 Index Laws Worksheet — Level 3 — Practice Set 2 — Answers

Use the index laws. Write answers with positive indices.

1.Evaluate: 8⁰

Answer: 1

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

2.Simplify: (x⁸)⁵

Answer: x⁴⁰

Multiply the indices: 8 × 5 = 40

3.Write 5⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 5¹ = 1 ÷ 5

4.Evaluate: 2⁰

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: 5x⁶ × 4x⁵

Answer: 20x¹¹

5 × 4 = 20; add the indices: 11

7.Simplify: 5x⁸ × 2x²

Answer: 10x¹⁰

5 × 2 = 10; add the indices: 10

8.Simplify: (x⁹)³

Answer: x²⁷

Multiply the indices: 9 × 3 = 27

9.Simplify: (x⁹)⁹

Answer: x⁸¹

Multiply the indices: 9 × 9 = 81

10.Simplify: 2x⁵ × 2x⁹

Answer: 4x¹⁴

2 × 2 = 4; add the indices: 14

11.Simplify: (x⁸)⁴

Answer: x³²

Multiply the indices: 8 × 4 = 32

12.Simplify: 5x⁴ × 2x⁹

Answer: 10x¹³

5 × 2 = 10; add the indices: 13

13.Evaluate: 4⁰

Answer: 1

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

14.Simplify: 5x⁶ × 3x⁶

Answer: 15x¹²

5 × 3 = 15; add the indices: 12

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