Year 8 Index Laws Worksheet — Level 2 — Answers

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

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Year 8 · Mathematics · Indices & Scientific Notation

Year 8 Index Laws Worksheet — Level 2 — Answers

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Use the index laws. Write answers with positive indices.

1.Simplify: (x⁶)²

Answer: x¹²

Multiply the indices: 6 × 2 = 12

2.Simplify: x⁸ × x⁷

Answer: x¹⁵

Add the indices: 8 + 7 = 15

3.Simplify: (x²)⁵

Answer: x¹⁰

Multiply the indices: 2 × 5 = 10

4.Simplify: x³ × x⁶

Answer: x⁹

Add the indices: 3 + 6 = 9

5.Simplify: x⁴ × x²

Answer: x⁶

Add the indices: 4 + 2 = 6

6.Simplify: 3x³ × 4x³

Answer: 12x⁶

3 × 4 = 12; add the indices: 6

7.Simplify: x⁵ × x⁵

Answer: x¹⁰

Add the indices: 5 + 5 = 10

8.Simplify: x⁵ ÷ x²

Answer: x³

Subtract the indices: 5 − 2 = 3

9.Simplify: 2x⁵ × 4x⁵

Answer: 8x¹⁰

2 × 4 = 8; add the indices: 10

10.Simplify: x³ × x⁵

Answer: x⁸

Add the indices: 3 + 5 = 8

11.Simplify: x¹⁰ ÷ x⁹

Answer: x¹

Subtract the indices: 10 − 9 = 1

12.Simplify: 4x² × 4x⁵

Answer: 16x⁷

4 × 4 = 16; add the indices: 7

13.Simplify: x⁷ ÷ x²

Answer: x⁵

Subtract the indices: 7 − 2 = 5

14.Simplify: (x⁹)⁸

Answer: x⁷²

Multiply the indices: 9 × 8 = 72

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