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

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

Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Indices & Scientific Notation

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

Use the index laws. Write answers with positive indices.

1.Evaluate: 50

Answer: 1

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

2.Simplify: (x4)2

Answer: x8

Multiply the indices: 4 × 2 = 8

3.Simplify: (x4)3

Answer: x12

Multiply the indices: 4 × 3 = 12

4.Simplify: 5x5 × 2x4

Answer: 10x9

5 × 2 = 10; add the indices: 9

5.Simplify: 3x7 × 5x7

Answer: 15x14

3 × 5 = 15; add the indices: 14

6.Simplify: (x3)6

Answer: x18

Multiply the indices: 3 × 6 = 18

7.Write 5−3 as a fraction.

Answer:

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

8.Simplify: (x7)7

Answer: x49

Multiply the indices: 7 × 7 = 49

9.Simplify: 3x5 × 3x2

Answer: 9x7

3 × 3 = 9; add the indices: 7

10.Simplify: (x6)5

Answer: x30

Multiply the indices: 6 × 5 = 30

11.Simplify: (x3)9

Answer: x27

Multiply the indices: 3 × 9 = 27

12.Write 10−3 as a fraction.

Answer:

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

13.Evaluate: 40

Answer: 1

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

14.Write 2−2 as a fraction.

Answer:

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

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