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

Algebraic index laws

Simplifying x^3 x x^4 and similar.

11 original questions, 38 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
  1. Simplify  x3 × x × x4
  2. Simplify  x7 ÷ x2
  3. Simplify  (x2)3
3 marks
Show answer
a) x8 b) x5 c) x6
2
  1. Write  25 × 23  as a single power of 2.
  2. Work out the value of  38 ÷ 35
  3. Write  (52)3 ÷ 54  as a single power of 5.
3 marks
Show answer
a) 28 b) 27 c) 52
3
  1. Simplify  t8 ÷ t3
  2. Simplify  (k4)5
  3. Simplify  12x6y34x2y
3 marks
Show answer
a) t5 b) k20 c) 3x4y2
4
  1. Simplify  5a3 × 4a6
  2. Simplify  (2c4)3
3 marks
Show answer
a) 20a9 b) 8c12
5
  1. Simplify  n−5 × n8
  2. Write down the value of 2−3
3 marks
Show answer
a) n3 b) 1/8
6
  1. Simplify  3x2y × 4xy3
  2. Simplify  20p5q2 ÷ 5p2q
4 marks
Show answer
a) 12x3y4 b) 4p3q
7

Find the value of n in each of these.

  1. 7n × 74 = 710
  2. 38 ÷ 3n = 35
2 marks
Show answer
a) n = 6 b) n = 3
8
  1. Simplify  (h5)2
  2. Simplify  15d7 ÷ 3d2
  3. Expand  3t(2t + 5)
4 marks
Show answer
a) h10 b) 5d5 c) 6t2 + 15t
9
  1. Simplify  15a4b65a2b2
  2. Simplify  (3p2q)39pq2
4 marks
Show answer
a) 3a2b4 b) 3p5q
10
  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
11
  1. Simplify  (5p4q)2
  2. Simplify  24m8 ÷ 6m2
  3. Solve  4x − 7 > 2x + 3
5 marks
Show answer
a) 25p8q2 b) 4m6 c) x > 5

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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