plumiLaws of indices: Edexcel GCSE Maths questions
Every Edexcel GCSE Maths exam question on N7 Laws of indices, 2017–2025, with its mark scheme and examiner’s report.
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All 35 questions on Laws of indices, as a list
- June 2025, Paper 2H, Q9 (2 marks): 3x n for all the values of x that are not zero. Find the value of a, the value of b and the value of n. a = b = n =
- June 2025, Paper 3H, Q11 (4 marks): 3 3 3 14 8 3 (a) Find the value of n. n = 2 in the form am 12 b where a and b are integers. (b) Write 64 m 3
- November 2024, Paper 1H, Q10 (4 marks): (a) Work out 25 8 × 2 3 3 1 5 (b) Find the value of 32
- November 2024, Paper 3H, Q9 (3 marks): (a) Simplify fully 2x 3y 5 × 7x 2y (b) Simplify (m2)–3
- June 2024, Paper 1H, Q20 (3 marks): 2 x y 2 2 3 2 Given that x + y = 8 work out the value of n. n =
- November 2023, Paper 1H, Q2 (4 marks): (a) (i) Write down the value of 50 (ii) Write down the value of 5–2 5 4 (b) Write 2 × 2 in the form 2n where n is an integer. 3 2
- November 2023, Paper 1H, Q14 (3 marks): Work out the value of 27 3 2
- June 2023, Paper 1H, Q11 (3 marks): Write − in the form ax by c where a, b and c are integers. x y xy 3 4 2 7 × 3
- June 2023, Paper 1H, Q14 (4 marks): (a) Write 1 16 in the form 4 n where n is an integer. 5 3 (b) Work out the value of 8 − 9 3 2
- June 2023, Paper 3H, Q1 (4 marks): (a) Simplify (m 2 ) 3 5×x 8 (b) Simplify x (c) Expand 4p ( p 2 + 3p)
- November 2022, Paper 1H, Q3 (2 marks): Simplify (2−5 × 28)2 Give your answer as a power of 2
- November 2022, Paper 1H, Q17 (2 marks): Work out the value of 27
- November 2022, Paper 3H, Q14 (5 marks): (a) Simplify fully (3x5y6)4 (b) Expand and simplify (x + 2)(x − 3)(x + 4)
- June 2022, Paper 1H, Q18 (4 marks): Work out the value of 2 − 3 You must show all your working.
- June 2022, Paper 2H, Q1 (5 marks): (a) Simplify (x3)5 (b) Expand and simplify 4(x + 3) + 7(4 − 2x) (c) Factorise fully 15x3 + 3x2y
- June 2022, Paper 3H, Q9 (4 marks): (a) Express as a power of 10 × 10 10 150 90 Liam was asked to express 2 as a power of 12 Liam wrote 2 = 12502 = 122500 Liam’s method is wrong. (b) Explain why.
- November 2021, Paper 1H, Q9 (4 marks): (a) Write down the value of 70 (b) Find the value of 3 × 36× 3–6 (c) Find the value of 2–4 1 (d) Find the value of 27 3
- November 2021, Paper 3H, Q12 (2 marks): ( ax x = n 6 ) 7 3 Work out the value of a and the value of n. a = n =
- November 2020, Paper 1H, Q11 (6 marks): (a) Find the value of 4 × 81 108 1 − (b) Find the value of 64 2 n (c) Write 3 n− as a power of 3 1 9
- November 2020, Paper 2H, Q10 (4 marks): (a) Simplify m 2 (b) Simplify 8 ( x − 4 ) ( x − 4 2 ) (c) Simplify (3n4w2)3
- November 2020, Paper 3H, Q1 (5 marks): (a) Simplify n3 × n5 . (b) Simplify c d 3 4 c d 2 . x > 7 (c) Solve 5 2
- November 2019, Paper 1H, Q19 (3 marks): Given that find the exact value of x. x =
- November 2019, Paper 3H, Q10 (4 marks): (a) Solve x x y (b) Simplify y
- June 2019, Paper 1H, Q8 (4 marks): (a) Work out an estimate for the value of × (2.3)6 = 148 correct to 3 significant figures. (b) Find the value of (0.23)6 correct to 3 significant figures. (c) F
- June 2019, Paper 1H, Q18 (5 marks): (a) Express in the form a 3 where a is an integer. 3 12 + 7 1 b ⎛ ⎞ (b) Express ⎠⎟ in the form c where b and c are integers. ⎝⎜ 3
- June 2019, Paper 3H, Q12 (1 mark): Patrick has to work out the exact value of 64 4 Patrick says, “ 1 1 4 16 ” 4 of 64 is 16 so 64 Explain what is wrong with what Patrick says.
- November 2018, Paper 1H, Q1 (2 marks): Work out the value of 3 7 3 2 3 3
- November 2018, Paper 1H, Q14 (4 marks): (a) Work out the value of ⎝⎜ ⎠⎟ 81 3a = 1 9 3b = 9 3 3c = 1 3 (b) Work out the value of a + b + c
- November 2018, Paper 3H, Q9 (8 marks): (a) Expand and simplify (x – 2)(2x + 3)(x + 1) 4 n y × y − 3 = y 2 y (b) Find the value of n. (c) Solve 5x2 – 4x – 3 = 0 Give your solutions correct to 3 signif
- June 2018, Paper 1H, Q9 (4 marks): (a) Write down the value of 36 2 (b) Write down the value of 230 2 − (c) Work out the value of 27 3
- June 2018, Paper 2H, Q1 (5 marks): (a) Simplify m3× m4 (b) Simplify (5np3)3 9 4 (c) Simplify 32 q r 3 4 q r
- November 2017, Paper 1H, Q10 (3 marks): (a) Write down the value of 100 2 2 (b) Find the value of 125 3
- November 2017, Paper 2H, Q6 (4 marks): S࣠ × S࣠x S࣠9 D )LQGWKHYDOXHRIx. x y E )LQGWKHYDOXHRIy. y aî bFDQEHZULWWHQLQWKHIRUP w F 6KRZWKDW
- June 2017, Paper 1H, Q12 (4 marks): (a) Find the value of 81 2 2 64 ⎛ ⎞ 3 (b) Find the value of ⎝⎜ ⎠⎟ 125
- June 2017, Paper 2H, Q18 (3 marks): 16 5 × 2 4 Work out the exact value of x.
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