Year 9 Index Laws Worksheet — Level 3 — Answers

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

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Year 9 · Mathematics · Indices & Scientific Notation

Year 9 Index Laws Worksheet — Level 3 — Answers

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Use the index laws. Write answers with positive indices.

1.Evaluate: 9⁰

Answer: 1

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

2.Write 5⁻¹ as a fraction.

Answer:

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

3.Simplify: 2x⁷ × 5x⁵

Answer: 10x¹²

2 × 5 = 10; add the indices: 12

4.Write 10⁻³ as a fraction.

Answer:

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

5.Simplify: (x⁶)⁴

Answer: x²⁴

Multiply the indices: 6 × 4 = 24

6.Evaluate: 3⁰

Answer: 1

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

7.Evaluate: 2⁰

Answer: 1

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

8.Simplify: 3x⁷ × 3x³

Answer: 9x¹⁰

3 × 3 = 9; add the indices: 10

9.Simplify: 3x⁶ × 2x⁹

Answer: 6x¹⁵

3 × 2 = 6; add the indices: 15

10.Simplify: 2x⁸ × 4x²

Answer: 8x¹⁰

2 × 4 = 8; add the indices: 10

11.Simplify: 2x⁷ × 2x⁶

Answer: 4x¹³

2 × 2 = 4; add the indices: 13

12.Simplify: (x⁸)⁸

Answer: x⁶⁴

Multiply the indices: 8 × 8 = 64

13.Write 5⁻² as a fraction.

Answer:

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

14.Evaluate: 5⁰

Answer: 1

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

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