Year 9 Index Laws Worksheet — Level 2 — 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 2 — Answers

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Use the index laws. Write answers with positive indices.

1.Simplify: x⁹ × x²

Answer: x¹¹

Add the indices: 9 + 2 = 11

2.Simplify: (x⁷)⁴

Answer: x²⁸

Multiply the indices: 7 × 4 = 28

3.Simplify: (x⁹)⁵

Answer: x⁴⁵

Multiply the indices: 9 × 5 = 45

4.Simplify: x¹⁰ ÷ x⁹

Answer: x¹

Subtract the indices: 10 − 9 = 1

5.Simplify: x⁹ × x⁷

Answer: x¹⁶

Add the indices: 9 + 7 = 16

6.Simplify: (x⁶)⁵

Answer: x³⁰

Multiply the indices: 6 × 5 = 30

7.Simplify: 4x⁵ × 2x⁵

Answer: 8x¹⁰

4 × 2 = 8; add the indices: 10

8.Simplify: 3x⁸ × 5x⁵

Answer: 15x¹³

3 × 5 = 15; add the indices: 13

9.Simplify: 4x⁴ × 5x⁹

Answer: 20x¹³

4 × 5 = 20; add the indices: 13

10.Simplify: x⁹ × x³

Answer: x¹²

Add the indices: 9 + 3 = 12

11.Simplify: x⁵ × x²

Answer: x⁷

Add the indices: 5 + 2 = 7

12.Simplify: 3x⁹ × 2x²

Answer: 6x¹¹

3 × 2 = 6; add the indices: 11

13.Simplify: x⁵ × x⁷

Answer: x¹²

Add the indices: 5 + 7 = 12

14.Simplify: x⁴ × x⁹

Answer: x¹³

Add the indices: 4 + 9 = 13

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