Robinson Tuition
Grade 7 · Higher · free GCSE maths worksheet

Fractional indices

Powers such as 8^(2/3).

13 original questions, 40 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

Work out, without a calculator, giving each answer as a fraction.

  1. (3 38)23
  2. (6 14)−32
3 marks
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a) 9/4 b) 8/125
2

Write down the value of 12112

1 mark
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11
3

Priya says that 2713 = 9 because 27 ÷ 3 = 9

Explain why Priya is wrong.

1 mark
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A power of 13 means the cube root, not dividing by 3. The cube root of 27 is 3, because 3 x 3 x 3 = 27.
4

Work out the value of (3625)12

2 marks
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65
5
  1. Work out the value of 823
  2. Work out the value of 25−12
  3. Work out the value of 10−2
3 marks
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a) 4 b) 1/5 c) 1/100
6

Simplify fully (27a9b6)23

3 marks
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9a6b4
7
  1. Work out the value of 64−23
  2. Work out the value of (8116)−34
4 marks
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a) 1/16 b) 8/27
8

9x = 127

Find the value of x.

3 marks
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-32
9
  1. 8n × 25 = 47
    Find the value of n.
  2. Write x√x as a single power of x.
4 marks
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a) 3 b) x(3/2)
10
  1. Work out the value of 27−23
  2. 4x = 32
    Find the value of x.
4 marks
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a) 1/9 b) 5/2
11
  1. Work out the value of (√3)6
  2. Work out the value of (64125)−23
  3. 32n = 1√8
    Find the value of n.
6 marks
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a) 27 b) 25/16 c) -3/10
12

(x + 2x−1)2 = x2 + a + bx−2 for all non-zero x.

Find the value of a and the value of b.

3 marks
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a) 4 b) 4
13

(27xa)13 = bx2 for all positive x.

Find the value of a and the value of b.

3 marks
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a) 6 b) 3

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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