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Year 10 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.

Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific Notation

Year 10 Index Laws Worksheet — Level 3 — Practice Set 4 — Answers

Use the index laws. Write answers with positive indices.

1.Simplify: 6x5 × 4x3

Answer: 24x8

6 × 4 = 24; add the indices: 8

2.Simplify: 3x5 × 4x3

Answer: 12x8

3 × 4 = 12; add the indices: 8

3.Evaluate: 20

Answer: 1

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

4.Evaluate: 70

Answer: 1

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

5.Simplify: 5x2 × 4x9

Answer: 20x11

5 × 4 = 20; add the indices: 11

6.Simplify: 6x6 × 3x2

Answer: 18x8

6 × 3 = 18; add the indices: 8

7.Write 5−2 as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 52 = 1 ÷ 25

8.Write 10−3 as a fraction.

Answer:

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

9.Simplify: (x4)7

Answer: x28

Multiply the indices: 4 × 7 = 28

10.Evaluate: 50

Answer: 1

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

11.Simplify: (x9)6

Answer: x54

Multiply the indices: 9 × 6 = 54

12.Simplify: 5x2 × 3x7

Answer: 15x9

5 × 3 = 15; add the indices: 9

13.Write 5−3 as a fraction.

Answer:

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

14.Simplify: (x9)5

Answer: x45

Multiply the indices: 9 × 5 = 45

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