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.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
2.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
3.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
5.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
6.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
7.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
8.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
9.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
10.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
11.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
12.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
13.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
14.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
15.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶

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