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Year 9 Index Laws Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: 5x4 × 4x7

Answer: 20x11

5 × 4 = 20; add the indices: 11

2.Simplify: (x5)2

Answer: x10

Multiply the indices: 5 × 2 = 10

3.Evaluate: 50

Answer: 1

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

4.Simplify: (x6)4

Answer: x24

Multiply the indices: 6 × 4 = 24

5.Write 3−3 as a fraction.

Answer:

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

6.Evaluate: 40

Answer: 1

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

7.Simplify: (x2)6

Answer: x12

Multiply the indices: 2 × 6 = 12

8.Simplify: (x6)5

Answer: x30

Multiply the indices: 6 × 5 = 30

9.Write 2−1 as a fraction.

Answer:

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

10.Simplify: 5x6 × 5x5

Answer: 25x11

5 × 5 = 25; add the indices: 11

11.Simplify: 6x3 × 2x8

Answer: 12x11

6 × 2 = 12; add the indices: 11

12.Simplify: (x5)8

Answer: x40

Multiply the indices: 5 × 8 = 40

13.Simplify: 3x4 × 3x3

Answer: 9x7

3 × 3 = 9; add the indices: 7

14.Evaluate: 30

Answer: 1

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

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