Year 8 Index Laws Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers

Use the index laws. Write answers with positive indices.

1.Write 2⁻² as a fraction.

Answer:

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

2.Evaluate: 6⁰

Answer: 1

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

3.Simplify: (x³)⁴

Answer: x¹²

Multiply the indices: 3 × 4 = 12

4.Evaluate: 2⁰

Answer: 1

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

5.Write 5⁻² as a fraction.

Answer:

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

6.Evaluate: 3⁰

Answer: 1

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

7.Simplify: (x⁸)⁴

Answer: x³²

Multiply the indices: 8 × 4 = 32

8.Simplify: 6x⁴ × 2x⁷

Answer: 12x¹¹

6 × 2 = 12; add the indices: 11

9.Simplify: (x⁹)²

Answer: x¹⁸

Multiply the indices: 9 × 2 = 18

10.Simplify: (x⁷)⁷

Answer: x⁴⁹

Multiply the indices: 7 × 7 = 49

11.Write 10⁻³ as a fraction.

Answer:

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

12.Simplify: (x⁵)⁹

Answer: x⁴⁵

Multiply the indices: 5 × 9 = 45

13.Simplify: 4x⁵ × 5x⁴

Answer: 20x⁹

4 × 5 = 20; add the indices: 9

14.Simplify: 5x⁴ × 4x⁴

Answer: 20x⁸

5 × 4 = 20; add the indices: 8

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