Powers and roots: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 1.4 Powers and roots, 2019–2025, with its mark scheme and examiner’s report.

All 108 questions on Powers and roots, as a list

June 2025 (R), Paper 1 Foundation, Q16 (2 marks): Find the lowest common multiple (LCM) of 45 and 70
June 2025 (R), Paper 1 Higher, Q1 (2 marks): Find the lowest common multiple (LCM) of 45 and 70
June 2025 (R), Paper 2 Foundation, Q18 (3 marks): Write 1400 as a product of powers of its prime factors. Show your working clearly.
June 2025 (R), Paper 2 Higher, Q2 (3 marks): Write 1400 as a product of powers of its prime factors. Show your working clearly.
June 2025 (R), Paper 2 Higher, Q16 (3 marks): Show that can be written in the form a where a and b are integers. − b 3 5 + 7 Show each stage of your working.
June 2025, Paper 1 Higher, Q15 (4 marks): where k is an integer. 3 3 (a) Find the value of k k = 21 (b) Show that can be written in the form c + d 3 − 2 where c and d are integers. Show each stage of yo
November 2024, Paper 1 Foundation, Q23 (2 marks): A 2 3 5 4 7 11 B 2 2 5 2 7 2 C 2 2 5 3 7 4 Find the highest common factor (HCF) of A, B and C Write your answer as a product of prime factors.
November 2024, Paper 1 Higher, Q6 (2 marks): A 2 3 5 4 7 11 B 2 2 5 2 7 2 C 2 2 5 3 7 4 Find the highest common factor (HCF) of A, B and C Write your answer as a product of prime factors.
November 2024, Paper 1 Higher, Q17 (4 marks): (a) Express 675 in the form n 27 where n is a positive integer. (b) Show that 5 − 2 can be written in the form a + b 2 where a and b 2 − 1 are integers.
June 2024 (R), Paper 1 Foundation, Q3 (4 marks): (a) Write a number in the box to make the statement correct. 5073 ÷ = 19 (b) Write a number in the box to make the statement correct. The cube root of is 14 Her
June 2024 (R), Paper 1 Higher, Q11 (4 marks): A 2 5 5 7 2 B 2 3 5 3 7 4 (a) Write down the highest common factor (HCF) of 5A and 2B Give your answer as a product of prime factors. A 2 5 5 7 2 B 2 3 5 3 7
June 2024 (R), Paper 1 Higher, Q17 (4 marks): (a) 4 k12 Find the value of n n = 7 (b) Express in the form where c and d are integers. c + d − 2 3 Show your working clearly.
June 2024 (R), Paper 2 Foundation, Q6 (5 marks): (a) Find the value of 3.42 (b) Find the cube root of 373 248 (c) Write 7 7 7 7 7 7 as a single power of 7 (d) Write one set of brackets in each calculatio
June 2024 (R), Paper 2 Foundation, Q17 (3 marks): Write 1400 as a product of powers of its prime factors. Show your working clearly.
June 2024 (R), Paper 2 Higher, Q1 (3 marks): Write 1400 as a product of powers of its prime factors. Show your working clearly.
June 2024, Paper 1 Foundation, Q5 (5 marks): Here is a list of numbers. 2 8 9 18 24 28 (a) From the numbers in the list, write down (i) an odd number (ii) a number that is a multiple of both 4 and 6 (iii)
June 2024, Paper 1 Foundation, Q18 (2 marks): Find the highest common factor (HCF) of 72 and 108 Show your working clearly.
June 2024, Paper 1 Higher, Q3 (2 marks): Find the highest common factor (HCF) of 72 and 108 Show your working clearly.
June 2024, Paper 1 Higher, Q17 (3 marks): Show that 1 5 can be written in the form a + b where a and b are integers. 3 5 Show each stage of your working clearly.
June 2024, Paper 2 Higher, Q23 (3 marks): Simplify 4 x 9 180 5 Give your answer in the form 5 w where w is an expression in terms of x Show each stage of your working clearly. for Question 24
November 2023, Paper 1 Foundation, Q1 (5 marks): Here is a list of numbers. 9 11 25 27 33 40 (a) From the numbers in the list, write down (i) an even number (ii) a cube number Here are the temperatures, in °C,
November 2023, Paper 1 Foundation, Q21 (2 marks): A and 3 3 B 6 2 4 5 7 11 5 7 11 Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.
November 2023, Paper 1 Higher, Q7 (2 marks): and B 6 2 4 A 5 3 7 3 11 5 7 11 Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.
November 2023, Paper 2 Higher, Q12 (4 marks): 2 7 5 x 4 4 (a) Calculate the value of x x = 2 (b) Simplify fully 125 p y 6 24 3
November 2023, Paper 2 Higher, Q15 (5 marks): (a) Use algebra to show that 0 372 . 110 + 125 80 (b) Express in the form n where n is an integer. 3 Show your working clearly.
June 2023 (R), Paper 1 Foundation, Q8 (4 marks): (a) Write down the prime number that lies between 90 and 100 (b) Find the cube root of 79 507 (c) Work out the value of 42 × 53
June 2023 (R), Paper 1 Foundation, Q17 (3 marks): Write 2250 as a product of powers of its prime factors. Show your working clearly.
June 2023 (R), Paper 1 Higher, Q1 (3 marks): Write 2250 as a product of powers of its prime factors. Show your working clearly.
June 2023 (R), Paper 2 Higher, Q16 (3 marks): Show that 2 3 can be written in the form a + a where a is an integer. 3 − 1 Show your working clearly.
June 2023, Paper 1 Foundation, Q23 (4 marks): (a) Write 300 as a product of its prime factors. Show your working clearly. A = 2 × 2 × 2 × 3 × 3 × 5 B = 2 × 2 × 3 × 3 × 3 × 5 (b) Find the lowest common multi
June 2023, Paper 1 Higher, Q8 (4 marks): (a) Write 300 as a product of its prime factors. Show your working clearly. A = 2 × 2 × 2 × 3 × 3 × 5 B = 2 × 2 × 3 × 3 × 3 × 5 (b) Find the lowest common multi
June 2023, Paper 1 Higher, Q15 (6 marks): (a) 2 2 n 3 16 2 Work out the value of n Show your working clearly. n = (b) Find 4% of 4.5 × 10 157 Give your answer in standard form.
June 2023, Paper 2 Higher, Q23 (4 marks): The diagram shows a cuboid with a square cross section. Diagram NOT accurately drawn x cm x cm (2 5 – 3) cm The volume of the cuboid is (13 + 6 5 ) cm3 Without
January 2023 (R), Paper 1 Higher, Q18 (4 marks): Solve Give your answer in the form a + b 3 where a and b are integers. Show your working clearly. x =
January 2023 (R), Paper 2 Foundation, Q21 (4 marks): (a) Find the highest common factor (HCF) of 200 and 420 A = 23 × 3 × 5 ×72 B = 2 × 32 × 7 C = 3 × 52 × 11 (b) Find the lowest common multiple (LCM) of A, B and
January 2023 (R), Paper 2 Higher, Q7 (4 marks): (a) Find the highest common factor (HCF) of 200 and 420 A = 23 × 3 × 5 ×72 B = 2 × 32 × 7 C = 3 × 52 × 11 (b) Find the lowest common multiple (LCM) of A, B and
January 2023, Paper 1 Foundation, Q4 (5 marks): (a) Write 0.8 as a percentage. % (b) Write down the value of the 3 in the number 4.7634 (c) Write these decimals in order of size. Start with the smallest decim
January 2023, Paper 1 Higher, Q12 (2 marks): 3 (a) Work out the value of m m = 5–10 ÷ 5– 4 = 5n (b) Work out the value of n n =
January 2023, Paper 2 Foundation, Q11 (4 marks): (a) Work out the value of (4 + 3 + 6)2 64 = 4n (b) Write down the value of n n = 9 3 . + 2 8 . 3 (c) Work out the value of 3 2 . × 1 2 . Write down all the figu
January 2023, Paper 2 Higher, Q17 (4 marks): Given that 8 m + 49 m − 9 m = k m where k is an integer and m is a prime number, (a) work out the value of k k = (b) Show that 5 − 18 can be written in the form
January 2023, Paper 2 Higher, Q26 (5 marks): Find the values of n such that 2 5 × × 10 n 2 n n 5 n 4 3 ( − ) 2 1 2 ( − ) = 1 20 2 Show clear algebraic working.
June 2022 (R), Paper 1 Higher, Q12 (3 marks): P = 3 3× 5 2× 7 2× 5 × 7 2 Q = 3 (a) Write down the highest common factor (HCF) of P and Q P = 3 3× 5 2× 7 Q = 3 2× 5 × 7 2 (b) Work out the value of P 3×Q Give
June 2022 (R), Paper 1 Higher, Q21 (4 marks): Express 3 8 in the form p + q where p and q are integers. ( ) 2 2 − 1 Show each stage of your working clearly. for Question 22
June 2022 (R), Paper 2 Foundation, Q6 (4 marks): (a) Find the value of (i) 31 36 . 3 (ii) 14 (b) Write a number on each dotted line to make the calculation correct. (i) 10 – × 2 = 4 (ii) (5 + ) × 3 = 36
June 2022 (R), Paper 2 Foundation, Q19 (3 marks): Write 1200 as a product of powers of its prime factors. Show your working clearly.
June 2022 (R), Paper 2 Higher, Q2 (3 marks): Write 1200 as a product of powers of its prime factors. Show your working clearly.
June 2022, Paper 1 Foundation, Q18 (4 marks): (a) Find the highest common factor (HCF) of 56 and 84 Show your working clearly. (b) Find the lowest common multiple (LCM) of 60 and 72 Show your working clearl
June 2022, Paper 1 Foundation, Q24 (4 marks): (a) Simplify 8 × (4t)0 x6 ÷ x−5 = xp (b) Find the value of p p = (c) Simplify fully (2k2m4) 3
June 2022, Paper 1 Higher, Q3 (4 marks): (a) Find the highest common factor (HCF) of 56 and 84 Show your working clearly. (b) Find the lowest common multiple (LCM) of 60 and 72 Show your working clearl
June 2022, Paper 1 Higher, Q9 (4 marks): (a) Simplify 8 × (4t)0 x6 ÷ x−5 = xp (b) Find the value of p p = (c) Simplify fully (2k2m4) 3
June 2022, Paper 1 Higher, Q16 (3 marks): Without using a calculator, show that 2 2 32 + 12 2 − 1 Show your working clearly.
June 2022, Paper 2 Higher, Q24 (3 marks): = 3 x × 6 9 n 2 + 8 Express x in terms of n Show your working clearly and simplify your expression. x =
January 2022 (R), Paper 1 Foundation, Q20 (4 marks): (a) Work out the lowest common multiple (LCM) of 36 and 120 A = 52 × 74 × 11p B = 5m × 7n–5 × 11 m, n and p are integers such that m > 2 n > 10 p > 1 (b) Find t
January 2022 (R), Paper 1 Higher, Q6 (4 marks): (a) Work out the lowest common multiple (LCM) of 36 and 120 A = 52 × 74 × 11p B = 5m × 7n–5 × 11 m, n and p are integers such that m > 2 n > 10 p > 1 (b) Find t
January 2022 (R), Paper 2 Higher, Q13 (3 marks): a = + 4 8 b = − 8 4 (a – b) (a + b) can be written in the form y 4 y Find the value of y Show your working clearly. y =
January 2022, Paper 2 Higher, Q17 (3 marks): Show that 3 + 2 can be written in the form a + b where a and b are integers.
November 2021, Paper 1 Foundation, Q19 (3 marks): Write 3.6 ´ 103 as a product of powers of its prime factors. Show your working clearly.
November 2021, Paper 1 Higher, Q7 (3 marks): Write 3.6 ´ 103 as a product of powers of its prime factors. Show your working clearly.
November 2021, Paper 2 Higher, Q17 (3 marks): Express in the form a + b where a and b are integers. 5 - 1 Show each stage of your working clearly.
June 2021, Paper 1 Higher, Q11 (4 marks): 2 × 16 = 2 x (a) Find the value of x. Show your working clearly. x = ( 11 − 6 5 ) n = 11 11 4 (b) Find the value of n. Show your working clearly. n =
June 2021, Paper 2 Foundation, Q15 (3 marks): Write 600 as a product of powers of its prime factors. Show your working clearly.
June 2021, Paper 2 Higher, Q1 (3 marks): Write 600 as a product of powers of its prime factors. Show your working clearly.
January 2021 (R), Paper 1 Foundation, Q24 (4 marks): A = 2 8× 3 5× 11 4 B = 2 6× 3 × 11 8 (a) Find the highest common factor (HCF) of A and B. (b) Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM a
January 2021 (R), Paper 1 Higher, Q9 (4 marks): A = 2 8× 3 5× 11 4 B = 2 6× 3 × 11 8 (a) Find the highest common factor (HCF) of A and B. (b) Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM a
January 2021 (R), Paper 1 Higher, Q12 (9 marks): (a) Simplify (16e (b) Write 2 x + 1 x − 2 as a single fraction in its simplest form. + 4 3 k + 3 = 16 × 2 k Given that 4 (c) find the value of k. Show your work
January 2021 (R), Paper 1 Higher, Q15 (5 marks): (a) Use algebra to show that 4.5. 7. = 4 19 33 2 can be written in the form a + a (b) Show that b 6 − 3 2 where a and b are integers. Show your working clearly.
January 2021 (R), Paper 2 Higher, Q19 (7 marks): (a) Simplify 8 × 4 Give your answer in the form 2 a where a is an integer. Show each stage of your working clearly. 4   4 −  =   1  Given that n 5 where
January 2021, Paper 2 Foundation, Q23 (2 marks): A = 2 4 × 3 × 5 4× 13 B = 2 Find the lowest common multiple (LCM) of A and B. Give your answer as a product of powers of prime numbers.
January 2021, Paper 2 Higher, Q9 (2 marks): A = 23× 32 × 52× 11 B = 24 × 3 × 54 × 13 Find the lowest common multiple (LCM) of A and B. Give your answer as a product of powers of prime numbers.
November 2020 (R), Paper 1 Foundation, Q14 (2 marks): Find the lowest common multiple (LCM) of 20 and 35
November 2020 (R), Paper 1 Higher, Q21 (5 marks): Given that M = 18 4 n × 2 3 ( n − 6 n ) × 3 2 1 4 ( − n ) 12 2 find the values of n for which M = 2
November 2020 (R), Paper 2 Foundation, Q9 (7 marks): (a) Work out 16 ÷ 4 + 3 × 8 (b) Find the cube root of 5832 (c) Write 85% as a decimal. (d) Write these fractions in order of size. Start with the smallest fract
November 2020 (R), Paper 2 Foundation, Q15 (3 marks): Write 880 as a product of powers of its prime factors. Show your working clearly.
November 2020 (R), Paper 2 Higher, Q2 (3 marks): Write 880 as a product of powers of its prime factors. Show your working clearly.
November 2020 (R), Paper 2 Higher, Q26 (5 marks): A, B, D and E are points on a circle. ABC and EDC are straight lines. Diagram NOT A accurately drawn B (2 + 5 ) cm C 2 5 cm D E (4 + 5 ) cm BC = (2 + 5 ) cm ED
November 2020, Paper 1 Foundation, Q23 (3 marks): A = 2 × 343 B = 16 × 337 (a) Find the highest common factor (HCF) of A and B. (b) Express the number A × B as a product of powers of its prime factors. Give you
November 2020, Paper 1 Higher, Q10 (3 marks): A = 2 × 343 B = 16 × 337 (a) Find the highest common factor (HCF) of A and B. (b) Express the number A × B as a product of powers of its prime factors. Give you
November 2020, Paper 1 Higher, Q19 (3 marks): Without using a calculator, rationalise the denominator of 3 − 7 Simplify your answer. You must show each stage of your working.
November 2020, Paper 2 Higher, Q12 (3 marks): Given that 3 x = 81 3 9 find the value of x. Show clear algebraic working. x =
January 2020 (R), Paper 1 Foundation, Q9 (4 marks): (a) Write 24.8635 correct to 3 significant figures. (b) Find the value of 50 41 . (c) Change 7 8 to a percentage. %
January 2020 (R), Paper 1 Foundation, Q16 (8 marks): (a) Make a the subject of d = g + 2ac (b) Factorise fully 9e f − 12 f (c) Expand and simplify (x + 2)(x − 5) (d) Simplify fully n × n 4 7 n 5
January 2020 (R), Paper 1 Higher, Q3 (8 marks): (a) Make a the subject of d = g + 2ac (b) Factorise fully 9e f − 12 f (c) Expand and simplify (x + 2)(x − 5) (d) Simplify fully n × n 4 7 n 5
January 2020 (R), Paper 1 Higher, Q13 (4 marks): (a) Use algebra to show that 0.57. 2. = 63 110 Given that y is a prime number, in the form a + b y 3 (b) express where a, b and c are integers. c − y 2 − y
January 2020 (R), Paper 2 Foundation, Q1 (5 marks): (a) Write in figures the number seventy thousand, two hundred and sixteen. (b) Write down a common factor of 20 and 30 (c) Write down a square number that is be
January 2020 (R), Paper 2 Foundation, Q12 (6 marks): (a) Simplify k + k + k + k f = 9 × 9 × 9 × 9 (b) (i) Write f as a single power of 9 (ii) Write f as a single power of 3 (c) Write 517 × 52 as a single power of
January 2020 (R), Paper 2 Higher, Q1 (3 marks): (a) Write 517 × 52 as a single power of 5 (b) Write 800 as a product of its prime factors. Show your working clearly.
January 2020, Paper 1 Higher, Q2 (2 marks): Find the lowest common multiple (LCM) of 28 and 105
January 2020, Paper 1 Higher, Q17 (6 marks): (a) Show that 6 + 2 12 12 7 + 4 3 Show each stage of your working. 2 − a (b) Simplify fully 27   12 3   t 15
January 2020, Paper 2 Foundation, Q17 (3 marks): (a) Simplify x 9 x 2 (b) Write 7 8 × 7 4 as a single power of 7 7 3
January 2020, Paper 2 Higher, Q1 (3 marks): (a) Simplify x 9 x 2 × (b) Write 7 8 7 4 as a single power of 7 7 3
January 2020, Paper 2 Higher, Q20 (3 marks): The area of a rectangle is 18 cm2 ( ) cm. The length of the rectangle is + 7 1 Without using a calculator and showing each stage of your working, find the width
June 2019 (R), Paper 1 Foundation, Q18 (5 marks): (a) Find the highest common factor (HCF) of 21 and 35 (b) Write 720 as a product of its prime factors. Show your working clearly. (c) Find the smallest whole nu
June 2019 (R), Paper 1 Higher, Q5 (4 marks): (a) Write 720 as a product of its prime factors. Show your working clearly. (b) Find the smallest whole number that 720 can be multiplied by to give a square nu
June 2019 (R), Paper 2 Foundation, Q23 (4 marks): A = 32 x 54x 7 B = 34 × 53 × 7 × 11 (a) Find the highest common factor (HCF) of A and B. (b) Find the lowest common multiple (LCM) of A and B.
June 2019 (R), Paper 2 Higher, Q8 (4 marks): A = 32 × 54 × 7 B = 34 × 53 × 7 × 11 (a) Find the highest common factor (HCF) of A and B. (b) Find the lowest common multiple (LCM) of A and B.
June 2019, Paper 1 Foundation, Q14 (4 marks): (a) Find the highest common factor (HCF) of 40 and 64 A = 2n × 3 × 5m (b) Write 8A as a product of powers of its prime factors.
June 2019, Paper 1 Higher, Q10 (2 marks): A = 2n × 3 × 5m Write 8A as a product of powers of its prime factors.
June 2019, Paper 2 Foundation, Q1 (4 marks): Start with the smallest number. -5 3 -8 1 (b) Write these numbers in order of size. Start with the smallest number. 2.5 2.85 2.082 2.28 2.805 (c) Find (i) the v
June 2019, Paper 2 Higher, Q16 (3 marks): Show that 4 + 8 can be written in the form a 2, where a and b are integers. + b 2 − 1 Show each stage of your working clearly and give the value of a and the va
January 2019 (R), Paper 1 Foundation, Q14 (2 marks): (a) Work out 64 × 36 (b) Work out 114
January 2019 (R), Paper 1 Foundation, Q24 (5 marks): N = 480 ´ 109 (a) Write N as a number in standard form. (b) Write N as a product of powers of its prime factors. Show your working clearly. (c) Find the largest
January 2019 (R), Paper 1 Higher, Q9 (5 marks): N = 480 ´ 109 (a) Write N as a number in standard form. (b) Write N as a product of powers of its prime factors. Show your working clearly. (c) Find the largest
January 2019 (R), Paper 1 Higher, Q18 (3 marks): Show that can be written in the form n , where n is an integer. + n − 8 2 Show your working clearly.
January 2019 (R), Paper 2 Higher, Q14 (6 marks): (a) Given that a = 3x and b = 3y express in terms of a or b or a and b, (i) 32x (ii) 3x + 4y (iii) 3y − 1 a = 3x and b = 3y ab = 2187 a2b = 177 147 (b) Work out
January 2019, Paper 1 Foundation, Q7 (6 marks): (a) Write down the prime number between 90 and 100 (b) Find the value of 36 (c) Find the cube root of 6859 8 4 . 9 1 . 2 + (d) (i) Work out the value of 4 1 . 0
January 2019, Paper 1 Higher, Q16 (4 marks): (a) Rationalise the denominator of a + b where a is an integer and b is a prime number. a 4 b − Simplify your answer. −5   y x m (b) Given that where x ≠ y =
January 2019, Paper 2 Foundation, Q20 (4 marks): (a) Find the highest common factor (HCF) of 96 and 120 A = 23 ´ 5 ´ 72 ´ 11 B = 24 ´ 7 ´ 11 C = 3 ´ 52 (b) Find the lowest common multiple (LCM) of A, B and C.
January 2019, Paper 2 Higher, Q6 (4 marks): (a) Find the highest common factor (HCF) of 96 and 120 A = 23 ´ 5 ´ 72 ´ 11 B = 24 ´ 7 ´ 11 C = 3 ´ 52 (b) Find the lowest common multiple (LCM) of A, B and C.

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