plumiLaws of indices: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on N7 Laws of indices, 2017–2025, with its mark scheme and examiner’s report.
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All 39 questions on Laws of indices, as a list
- June 2025, Paper 1H, Q19 (5 marks): (a) Work out the value of − 3 2 9 16 Answer 19 (b) 125 = 5n Work out the value of n. n =
- November 2024, Paper 1H, Q22 (3 marks): Match each expression on the left to the correct expression on the right. One has been done for you. 7n = x 7–n 72n 7n + 1 n 1 2 7 7x x 1 1 2 x x x2
- June 2024, Paper 2H, Q6 (1 mark): Work out (2.5 × 104)–3 Give your answer in standard form. Answer
- June 2024, Paper 3H, Q17 (4 marks): (a) a and b are different prime numbers. a3 × b2 = 200 Work out the value of a4 × b Answer 17 (b) c and d are different prime numbers. Circle the equation for w
- November 2023, Paper 1H, Q5 (3 marks): Work out the value of (82 × 8) ÷ (89 ÷ 85) Give your answer as a decimal. Answer
- November 2023, Paper 1H, Q26 (4 marks): (a) Work out the value of 4 1 16 1 5 Answer 26 (b) Write ( ) m 2.5 49 as a power of 7 in terms of m. Answer
- June 2023, Paper 1H, Q7 (3 marks): 2a × 3 × 52 = 600 Work out the value of a. You must show your working. a =
- November 2022, Paper 1H, Q2 (1 mark): Circle the value of ( ) 4 6 12 36 10 24
- November 2022, Paper 1H, Q11 (3 marks): Write (36 × 35) : 37 in the form n : 1 where n is an integer. Answer : 1
- November 2022, Paper 1H, Q19 (4 marks): (a) Work out the value of 2 5 4 − Answer 19 (b) Work out the value of 3 2 9 100 Answer
- June 2022, Paper 1H, Q6 (4 marks): (a) Work out 7 12 3 3 Give your answer as a whole number. Answer 6 (b) Simplify 8 × 26 × 24 Give your answer as a power of 2 Answer
- June 2022, Paper 2H, Q15 (2 marks): In the grid, the product of each row, column and diagonal is 1 1 4 4 1 8 Complete the grid.
- June 2022, Paper 2H, Q22 (1 mark): Circle the reciprocal of 85 8–5 5–8 –85 58
- November 2021, Paper 1H, Q1 (1 mark): Simplify a 3 5 Circle your answer. 8a 15a a8 a15
- November 2021, Paper 1H, Q22 (3 marks): Work out the value of 2 7 5 − Give your answer as a mixed number. Answer
- November 2021, Paper 3H, Q18 (1 mark): Simplify w1 × w0 Circle your answer. 1 0 w w2
- November 2021, Paper 3H, Q23 (2 marks): The equation of a curve is y = 16x 23 (a) Circle the point that lies on the curve. (2, 32) (32, 2) (2, 256) (256, 2) 23 (b) A different point on the curve has y
- November 2021, Paper 3H, Q24 (1 mark): ab = 3 where a is an integer and b is a proper fraction. Work out one possible pair of values of a and b. a = b =
- November 2020, Paper 1H, Q20 (3 marks): (a) Write down the value of 70 Answer 20 (b) Work out the value of – 3 5 32 Answer
- November 2019, Paper 1H, Q4 (1 mark): Circle the expression equivalent to (2x)4 2x4 6x4 8x4 16x4
- November 2019, Paper 1H, Q8 (3 marks): Write 27 × 7 2 3 as a single power of 3 Answer
- November 2019, Paper 1H, Q28 (2 marks): Work out the value of 1 2 100 − Answer
- June 2019, Paper 1H, Q2 (1 mark): Work out the value of 2 3 2 1 Circle your answer. 9 4 1 3 1 3 9 4 2 9 7 2
- June 2019, Paper 1H, Q8 (3 marks): Work out the value of (312 ÷ 35) ÷ (32 × 3) Answer
- June 2019, Paper 1H, Q23 (3 marks): Simplify 84 ÷ 5 2 32 Give your answer in the form 2m where m is an integer. Answer
- November 2018, Paper 1H, Q1 (1 mark): Simplify 2 4 5 Circle your answer. 56 58 256 258
- November 2018, Paper 1H, Q9 (4 marks): 3 2 2 3 6 8 125a + = Work out the value of a. Answer
- November 2018, Paper 1H, Q17 (2 marks): Work out the exact value of 3 4 3 − Answer
- November 2018, Paper 2H, Q27 (3 marks): The point 64 1 3, lies on the curve y = k x where k is a constant. Show that the point 2 1 , 2 1 lies on the curve.
- June 2018, Paper 1H, Q24 (5 marks): (a) Work out the value of 214 ÷ 2 9 2 Give your answer as a fraction in its simplest form. Answer 24 (b) Work out the value of 2 3 25 Answer
- November 2017, Paper 1H, Q3 (1 mark): Circle the expression that is equivalent to 2 5 4 a 16a10 16a7 8a10 8a7
- November 2017, Paper 1H, Q30 (5 marks): (a) Work out the value of 4 1 81 − Answer 30 (b) Write 16 × x 2 8 as a power of 2 in terms of x. Answer
- November 2017, Paper 3H, Q21 (3 marks): N is a number. As a product of prime factors in index form N = 2 × 34 × y3 Work out 3N 2 as a product of prime factors in index form. Give your answer in terms
- June 2017, Paper 1H, Q1 (1 mark): Simplify 25 × 23 Circle your answer. 48 28 215 415
- June 2017, Paper 1H, Q24 (3 marks): (a) Work out 4 1 12 as an improper fraction. Answer 24 (b) Work out 3 16 as a power of 2 Answer
- June 2017, Paper 3H, Q12 (2 marks): 4 b r a = 16r20 where a and b are positive integers. Work out a and b a = b =
- Specimen, Paper 1H, Q2 (1 mark): Simplify 3 4 3 4 Circle the answer. 38 9 8 3 16 9 16
- Specimen, Paper 3H, Q12 (3 marks): Tick whether each statement is true or false. Give a reason for your answer. 12 (a) When x2 = 16 the only value that x can be is 4 True False Reason 12 (b) When
- Specimen, Paper 3H, Q14 (2 marks): (a) The nth term of a sequence is 2n + 2n – 1 Work out the 10th term of the sequence. Answer 14 (b) The nth term of a different sequence is 4(2n + 2n – 1) Circl
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