Success TutoringWorksheets

Year 10 Index Laws Worksheet — Level 3 — Practice Set 3 — 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 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.Write 10−3 as a fraction.

Answer:

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

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.Write 3−2 as a fraction.

Answer:

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

6.Evaluate: 80

Answer: 1

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

7.Simplify: (x8)6

Answer: x48

Multiply the indices: 8 × 6 = 48

8.Evaluate: 90

Answer: 1

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

9.Simplify: 6x9 × 3x3

Answer: 18x12

6 × 3 = 18; add the indices: 12

10.Simplify: (x7)3

Answer: x21

Multiply the indices: 7 × 3 = 21

11.Write 10−2 as a fraction.

Answer:

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

12.Simplify: (x6)6

Answer: x36

Multiply the indices: 6 × 6 = 36

13.Evaluate: 20

Answer: 1

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

14.Simplify: (x3)2

Answer: x6

Multiply the indices: 3 × 2 = 6

Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.