Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Negative indices

Evaluating and simplifying powers like 2^-3.

14 original questions, 41 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 the value of

  1. 5−2
  2. 4−3
2 marks
Show answer
a) 1/25 b) 1/64
2
  1. Work out the value of 90
  2. Work out the value of 2−4
2 marks
Show answer
a) 1 b) 1/16
3

Write each number as a power with a negative index.

  1. Write 181 as a power of 3.
  2. Write 1125 as a power of 5.
2 marks
Show answer
a) 3-4 b) 5-3
4

Work out the value of (35 × 3−2) ÷ 3

2 marks
Show answer
9
5

Work out the value of

  1. (23)−2
  2. (14)−3
3 marks
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a) 9/4 b) 64
6
  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
Show answer
a) 4 b) 1/5 c) 1/100
7

Work out the value of the letter in each equation.

  1. 2k = 132
  2. 5m = 0.04
3 marks
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a) k = -5 b) m = -2
8

Work out the value of

  1. 49−12
  2. 27−23
  3. 32−35
3 marks
Show answer
a) 1/7 b) 1/9 c) 1/8
9

Simplify

  1. 3x−2 × 2x5
  2. 12x3 ÷ 4x−2
  3. (2x−2)3
4 marks
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a) 6x3 b) 3x5 c) 8x-6
10

Work out the value of

  1. (49)−12
  2. (18)−23
4 marks
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a) 3/2 b) 4
11
  1. Simplify  n−5 × n8
  2. Write down the value of 2−3
3 marks
Show answer
a) n3 b) 1/8
12

Write 52x3 in the form axn, where a and n are constants.

Write down the value of a and the value of n.

2 marks
Show answer
a) a = 5/2 b) n = -3
13

Expand and simplify

  1. x−2(x5 + 4x2)
  2. 3x−1(2x3 − 5x)
4 marks
Show answer
a) x3 + 4 b) 6x2 - 15
14
  1. Write down the value of 170
  2. Write down the value of 4−2
  3. Simplify  (m−3)4 × m14
4 marks
Show answer
a) 1 b) 1/16 c) m2

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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