Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Index laws with numbers

Multiplying and dividing powers of the same base.

13 original questions, 33 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down the value of 1003

1 mark
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1000000
2
  1. Write down the value of 50
  2. Write down the value of 2−3 as a fraction
2 marks
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a) 1 b) 1/8
3
  1. Write 74 × 73 as a single power of 7
  2. Write 129 ÷ 124 as a single power of 12
2 marks
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a) 77 b) 125
4

Write (43 × 45) ÷ 42 as a single power of 4

2 marks
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46
5
  1. Write (53)4 as a single power of 5
  2. Write down the value of 80
2 marks
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a) 512 b) 1
6
  1. Write down the value of 10−3 as a decimal.
  2. Write down the value of 1002
  3. Write 19 as a power of 3.
3 marks
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a) 0.001 b) 10000 c) 3-2
7

Work out the value of (35 × 3−2) ÷ 3

2 marks
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9
8

Work out the value of (25 × 2−2) ÷ 22

3 marks
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2
9

26 × 2k23  =  211

Find the value of k.

3 marks
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8
10
  1. 3k ÷ 32 = 36. Find the value of k.
  2. (23)m = 212. Find the value of m.
3 marks
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a) 8 b) 4
11
  1. Write 7−2 × 7−3 as a single power of 7
  2. Work out the value of 7−2 × 7−3 as a fraction.
3 marks
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a) 7-5 b) 1/16807
12
  1. Write 8 × 24 as a power of 2
  2. Write 25 × 53 as a power of 5
3 marks
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a) 27 b) 55
13
  1. Write (72)5 as a single power of 7
  2. Zara writes

    34 × 35 = 99

    Explain what Zara has done wrong, and write down the correct answer as a single power.

4 marks
Show answer
a) 710 b) 39 (Zara wrongly changed the base from 3 to 9)

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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