Year 8 Index Laws Worksheet — Level 3 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Indices & Scientific Notation

Year 8 Index Laws Worksheet — Level 3 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: 4x⁸ × 3x⁶

Answer: 12x¹⁴

4 × 3 = 12; add the indices: 14

2.Evaluate: 2⁰

Answer: 1

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

3.Write 2⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2² = 1 ÷ 4

4.Evaluate: 9⁰

Answer: 1

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

5.Simplify: 2x⁷ × 4x⁶

Answer: 8x¹³

2 × 4 = 8; add the indices: 13

6.Write 3⁻² as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 3² = 1 ÷ 9

7.Simplify: (x⁴)⁹

Answer: x³⁶

Multiply the indices: 4 × 9 = 36

8.Simplify: 4x⁵ × 2x³

Answer: 8x⁸

4 × 2 = 8; add the indices: 8

9.Write 2⁻³ as a fraction.

Answer:

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

10.Evaluate: 8⁰

Answer: 1

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

11.Simplify: 5x² × 3x³

Answer: 15x⁵

5 × 3 = 15; add the indices: 5

12.Write 2⁻¹ as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 2¹ = 1 ÷ 2

13.Simplify: (x²)⁹

Answer: x¹⁸

Multiply the indices: 2 × 9 = 18

14.Simplify: 6x² × 4x⁴

Answer: 24x⁶

6 × 4 = 24; add the indices: 6

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