EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Algebraic Indices
Algebraic indices · Algebra · Lesson 1 of 7 · 11 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [1 mark]
Simplify m⁵ × m³
Question 2 NON-CALCULATOR [1 mark]
Simplify (p⁴)³
Question 3 NON-CALCULATOR [2 marks]
Simplify 4x²y³ × 3x⁵y
Question 4 NON-CALCULATOR [2 marks]
Simplify (2a³b)⁵
Question 5 NON-CALCULATOR · HIGHER [2 marks]
Simplify (64x⁶)^(2/3)
Question 6 NON-CALCULATOR · HIGHER [3 marks]
Solve 9^x = 27^(x−1)
Answers
Check your answer only once you have written one.
Question 1 [1 mark]
m⁸
▸ m⁸ B1
Question 2 [1 mark]
p¹²
▸ p¹² B1
Question 3 [2 marks]
12x⁷y⁴
▸ 12x⁷y⁴ B2
▸ Two of 12, x⁷ and y⁴ in a single term B1
Question 4 [2 marks]
32a¹⁵b⁵
▸ 32a¹⁵b⁵ B2
▸ Two of 32, a¹⁵ and b⁵ in a single term B1
Question 5 [2 marks]
64^(2/3) = (∛64)² = 4² = 16 and (x⁶)^(2/3) = x⁴, so 16x⁴.
▸ 16x⁴ B2
▸ 16 or x⁴ in a single term B1
Question 6 [3 marks]
9 = 3² and 27 = 3³, so 3^(2x) = 3^(3x−3). Then 2x = 3x − 3, so x = 3.
▸ Both sides written as powers of 3 M1
▸ 2x = 3x − 3 M1
▸ x = 3 A1