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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.Write 2−1 as a fraction.

Answer:

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

2.Simplify: (x5)7

Answer: x35

Multiply the indices: 5 × 7 = 35

3.Simplify: 6x7 × 2x2

Answer: 12x9

6 × 2 = 12; add the indices: 9

4.Simplify: (x3)4

Answer: x12

Multiply the indices: 3 × 4 = 12

5.Write 5−1 as a fraction.

Answer:

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

6.Evaluate: 40

Answer: 1

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

7.Simplify: (x2)7

Answer: x14

Multiply the indices: 2 × 7 = 14

8.Simplify: (x5)2

Answer: x10

Multiply the indices: 5 × 2 = 10

9.Write 3−1 as a fraction.

Answer:

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

10.Simplify: (x7)5

Answer: x35

Multiply the indices: 7 × 5 = 35

11.Simplify: (x9)3

Answer: x27

Multiply the indices: 9 × 3 = 27

12.Evaluate: 30

Answer: 1

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

13.Simplify: 5x2 × 4x5

Answer: 20x7

5 × 4 = 20; add the indices: 7

14.Simplify: (x2)4

Answer: x8

Multiply the indices: 2 × 4 = 8

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