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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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Year 10 · Mathematics · Indices & Scientific Notation

Year 10 Index Laws Worksheet — Level 3 — Answers

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Use the index laws. Write answers with positive indices.

1.Write 5−1 as a fraction.

Answer:

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

2.Evaluate: 50

Answer: 1

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

3.Write 2−1 as a fraction.

Answer:

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

4.Write 3−1 as a fraction.

Answer:

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

5.Evaluate: 20

Answer: 1

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

6.Simplify: 2x6 × 5x2

Answer: 10x8

2 × 5 = 10; add the indices: 8

7.Write 2−3 as a fraction.

Answer:

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

8.Evaluate: 30

Answer: 1

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

9.Simplify: 4x3 × 4x9

Answer: 16x12

4 × 4 = 16; add the indices: 12

10.Simplify: 2x3 × 5x8

Answer: 10x11

2 × 5 = 10; add the indices: 11

11.Write 10−1 as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 101 = 1 ÷ 10

12.Write 5−3 as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 53 = 1 ÷ 125

13.Evaluate: 70

Answer: 1

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

14.Simplify: 4x3 × 2x8

Answer: 8x11

4 × 2 = 8; add the indices: 11

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