Year 10 Index Laws Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.

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Year 10 · Mathematics · Indices & Scientific Notation

Year 10 Index Laws Worksheet — Level 3 — Answers

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Use the index laws. Write answers with positive indices.

1.Simplify: 3x³ × 4x⁶

Answer: 12x⁹

3 × 4 = 12; add the indices: 9

2.Simplify: (x⁹)³

Answer: x²⁷

Multiply the indices: 9 × 3 = 27

3.Simplify: 4x⁸ × 3x²

Answer: 12x¹⁰

4 × 3 = 12; add the indices: 10

4.Write 3⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 3¹ = 1 ÷ 3

5.Simplify: 4x⁷ × 4x⁷

Answer: 16x¹⁴

4 × 4 = 16; add the indices: 14

6.Simplify: (x⁹)²

Answer: x¹⁸

Multiply the indices: 9 × 2 = 18

7.Simplify: (x⁹)⁸

Answer: x⁷²

Multiply the indices: 9 × 8 = 72

8.Write 3⁻² as a fraction.

Answer:

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

9.Evaluate: 9⁰

Answer: 1

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

10.Evaluate: 8⁰

Answer: 1

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

11.Simplify: (x⁸)⁸

Answer: x⁶⁴

Multiply the indices: 8 × 8 = 64

12.Write 5⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 5² = 1 ÷ 25

13.Simplify: (x³)⁶

Answer: x¹⁸

Multiply the indices: 3 × 6 = 18

14.Evaluate: 3⁰

Answer: 1

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

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