Success TutoringWorksheets

Year 8 Index Laws Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 8 indices & scientific notation worksheet.

Download answers PDFPrint answersBack to worksheet

Year 8 · Mathematics · Indices & Scientific Notation

Year 8 Index Laws Worksheet — Level 3 — Answers

Success Tutoring

Use the index laws. Write answers with positive indices.

1.Simplify: 6x3 × 4x3

Answer: 24x6

6 × 4 = 24; add the indices: 6

2.Write 5−1 as a fraction.

Answer:

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

3.Write 2−1 as a fraction.

Answer:

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

4.Evaluate: 40

Answer: 1

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

5.Simplify: (x8)8

Answer: x64

Multiply the indices: 8 × 8 = 64

6.Evaluate: 70

Answer: 1

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

7.Write 2−2 as a fraction.

Answer:

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

8.Simplify: (x6)9

Answer: x54

Multiply the indices: 6 × 9 = 54

9.Write 10−1 as a fraction.

Answer:

A negative index means the reciprocal: 1 ÷ 101 = 1 ÷ 10

10.Evaluate: 90

Answer: 1

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

11.Simplify: 6x4 × 5x4

Answer: 30x8

6 × 5 = 30; add the indices: 8

12.Simplify: (x5)8

Answer: x40

Multiply the indices: 5 × 8 = 40

13.Simplify: (x7)3

Answer: x21

Multiply the indices: 7 × 3 = 21

14.Write 3−3 as a fraction.

Answer:

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

worksheets.successtutoring.com · Free to print and share 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.

Great work. Here's what to try next: