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Year 9 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 9 indices & scientific notation worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Indices & Scientific Notation

Year 9 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: 6x4 × 2x8

Answer: 12x12

6 × 2 = 12; add the indices: 12

2.Write 10−2 as a fraction.

Answer:

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

3.Write 3−3 as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 33 = 1 ÷ 27

4.Simplify: (x9)2

Answer: x18

Multiply the indices: 9 × 2 = 18

5.Evaluate: 20

Answer: 1

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

6.Simplify: (x4)9

Answer: x36

Multiply the indices: 4 × 9 = 36

7.Write 5−3 as a fraction.

Answer:

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

8.Write 2−1 as a fraction.

Answer:

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

9.Simplify: (x7)8

Answer: x56

Multiply the indices: 7 × 8 = 56

10.Write 3−2 as a fraction.

Answer:

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

11.Simplify: (x5)4

Answer: x20

Multiply the indices: 5 × 4 = 20

12.Simplify: (x4)7

Answer: x28

Multiply the indices: 4 × 7 = 28

13.Evaluate: 80

Answer: 1

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

14.Write 2−3 as a fraction.

Answer:

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

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