Robinson Tuition
Year 8 · Key Stage 3 · free KS3 maths worksheet

Powers, roots and index laws

12 original questions, 28 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Here is a list of numbers.

6   8   9   16   21   27   28   49   125

From the list, write down

  1. the square numbers
  2. the cube numbers
  3. the triangle numbers
3 marks
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a) 9, 16, 49 b) 8, 27, 125 c) 6, 21, 28
2

Write down the square number that is between 30 and 45

1 mark
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36
3
  1. Write 5 × 5 × 5 × 5 using index notation.
  2. Work out the value of 34
  3. Ruby says, "23 = 6". Explain why Ruby is wrong.
3 marks
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a) 54 b) 81 c) 23 means 2 × 2 × 2 = 8, Ruby worked out 2 × 3
4

Work out the value of 3√64

1 mark
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4
5

You are told that 172 = 289 and 63 = 216

Write down the value of

  1. √289
  2. 3√216
  3. √2.89
3 marks
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a) 17 b) 6 c) 1.7
6

Use your calculator to work out the value of 4.63

1 mark
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97.336
7

Use your calculator to work out

(2.42 + 1.8) ÷ 0.53

Write down all the figures on your calculator display.

2 marks
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60.48
8
  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
9
  1. Write 23 × 24 as a single power of 2
  2. Jamal says, "23 + 24 = 27".
    Show that Jamal is wrong.
3 marks
Show answer
a) 27 b) 23 + 24 = 8 + 16 = 24, but 27 = 128, so they are not equal
10

Simplify

  1. x4 × x6
  2. y9 ÷ y3
  3. (m2)5
3 marks
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a) x10 b) y6 c) m10
11

Write down the value of

  1. 50
  2. 4−1
  3. 912
3 marks
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a) 1 b) 1/4 c) 3
12

26 × 2k23  =  211

Find the value of k.

3 marks
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8

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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