Year 11 Index Laws Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.

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Year 11 · Mathematics · Indices & Scientific Notation

Year 11 Index Laws Worksheet — Level 3 — Answers

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Use the index laws. Write answers with positive indices.

1.Evaluate: 5⁰

Answer: 1

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

2.Simplify: (x⁵)⁵

Answer: x²⁵

Multiply the indices: 5 × 5 = 25

3.Write 5⁻¹ as a fraction.

Answer:

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

4.Simplify: (x⁸)³

Answer: x²⁴

Multiply the indices: 8 × 3 = 24

5.Simplify: (x⁶)⁴

Answer: x²⁴

Multiply the indices: 6 × 4 = 24

6.Write 2⁻³ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2³ = 1 ÷ 8

7.Simplify: 4x⁷ × 2x³

Answer: 8x¹⁰

4 × 2 = 8; add the indices: 10

8.Evaluate: 3⁰

Answer: 1

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

9.Simplify: 5x³ × 4x⁹

Answer: 20x¹²

5 × 4 = 20; add the indices: 12

10.Simplify: 6x⁹ × 3x⁹

Answer: 18x¹⁸

6 × 3 = 18; add the indices: 18

11.Simplify: 5x² × 5x⁴

Answer: 25x⁶

5 × 5 = 25; add the indices: 6

12.Simplify: 2x⁵ × 5x⁹

Answer: 10x¹⁴

2 × 5 = 10; add the indices: 14

13.Simplify: (x⁷)⁷

Answer: x⁴⁹

Multiply the indices: 7 × 7 = 49

14.Simplify: 4x⁸ × 4x⁵

Answer: 16x¹³

4 × 4 = 16; add the indices: 13

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