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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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific Notation

Year 10 Index Laws Worksheet — Level 3 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: (x⁸)³

Answer: x²⁴

Multiply the indices: 8 × 3 = 24

2.Simplify: 5x⁹ × 5x⁹

Answer: 25x¹⁸

5 × 5 = 25; add the indices: 18

3.Evaluate: 9⁰

Answer: 1

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

4.Simplify: 2x⁸ × 3x⁵

Answer: 6x¹³

2 × 3 = 6; add the indices: 13

5.Simplify: 3x² × 3x²

Answer: 9x⁴

3 × 3 = 9; add the indices: 4

6.Write 10⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 10² = 1 ÷ 100

7.Simplify: (x⁵)⁵

Answer: x²⁵

Multiply the indices: 5 × 5 = 25

8.Simplify: 4x⁶ × 2x²

Answer: 8x⁸

4 × 2 = 8; add the indices: 8

9.Write 5⁻² as a fraction.

Answer:

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

10.Write 10⁻³ as a fraction.

Answer:

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

11.Write 3⁻¹ as a fraction.

Answer:

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

12.Simplify: 2x⁴ × 5x⁵

Answer: 10x⁹

2 × 5 = 10; add the indices: 9

13.Simplify: 3x⁸ × 5x⁶

Answer: 15x¹⁴

3 × 5 = 15; add the indices: 14

14.Evaluate: 6⁰

Answer: 1

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

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