EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Calculating with Powers
Calculating with powers (indices) · Number · Lesson 4 of 7 · 12 marks · 25 minutes
Name Date
Answer all questions. Show your working. Questions 1 to 5 are non-calculator.
Question 1 NON-CALCULATOR [1 mark]
Write down the value of 3⁴.
Question 2 NON-CALCULATOR [2 marks]
Write (5⁶ × 5³)/5⁴ as a single power of 5.
Question 3 NON-CALCULATOR [2 marks]
Work out 2³ × 5² − √144
Question 4 NON-CALCULATOR [2 marks]
2ⁿ = 4⁵ ÷ 2³. Find the value of n.
Question 5 NON-CALCULATOR · SHOW THAT [3 marks]
Show that 9⁴ × 27² = 3¹⁴
Question 6 CALCULATOR [2 marks]
(a) Work out (2.7³ − √18.5)/1.4². Write down all the figures on your calculator display. (b) Give your answer to part (a) correct to 3 significant figures.
Answers
Check your answer only once you have written one.
Question 1 [1 mark]
81
▸ 81 B1
Question 2 [2 marks]
5⁶ × 5³ = 5⁹, and 5⁹ ÷ 5⁴ = 5⁵
▸ 5⁹ seen, or a correct method for dividing M1
▸ 5⁵ A1
Question 3 [2 marks]
8 × 25 − 12 = 200 − 12 = 188
▸ Two of 8, 25 and 12 seen, or 200 seen M1
▸ 188 A1
Question 4 [2 marks]
4⁵ = (2²)⁵ = 2¹⁰, so 2¹⁰ ÷ 2³ = 2⁷ and n = 7.
▸ 4⁵ written as 2¹⁰, or 1024 ÷ 8 = 128 M1
▸ n = 7 A1
Question 5 [3 marks]
9 = 3², so 9⁴ = (3²)⁴ = 3⁸. 27 = 3³, so 27² = (3³)² = 3⁶. 3⁸ × 3⁶ = 3¹⁴.
▸ 9 = 3² or 27 = 3³ used M1
▸ 3⁸ and 3⁶ M1
▸ Fully correct working leading to 3¹⁴ A1
Question 6 [2 marks]
(a) 7.847876207 (b) 7.85
▸ (a) 7.8478… (at least 5 figures) B1
▸ (b) 7.85, follow through from (a) B1