Printable · GCSE Higher · ages 14-16

Calculating with roots and indices worksheet — GCSE Higher

Fifteen questions on "calculating with roots and indices" — DfE statement N7. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

part HigherNon-calculator

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Calculating with roots and indices worksheet — GCSE Higher

Maths · GCSE Higher · N7 · Calculating with roots and indices · Non-calculator · 15 questions

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1.Simplify x⁷ × x⁴, giving your answer as a single power of x.
(a)x¹¹
(b)11x
(c)x³
(d)x²⁸
2.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
3.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
4.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
5.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
6.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
7.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.
(a)22 mm
(b)242 mm
(c)60.5 mm
(d)11 mm
8.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
9.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
10.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾
(a)x
(b)x⁽³⁄¹⁶⁾
(c)x³
(d)x⁽¹⁄²⁾
11.Work out the value of $2^{3} + 3^{2}$ .
(a)17
(b)72
(c)12
(d)−1
12.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.
(a)They are equal
(b)3²⁰ is larger
(c)2³⁰ is larger
(d)They cannot be compared without a calculator
13.Simplify (3a²)² × (2a)³
(a)17a⁷
(b)72a¹²
(c)36a⁷
(d)72a⁷
14.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
15.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4

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