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.

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Calculating with roots and indices worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

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 √49 + ∛27
(a)10
(b)34
(c)16
(d)21
3.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
5.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
6.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
7.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
8.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
9.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
10.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.
(a)5 cm
(b)50 cm
(c)25 cm
(d)125 cm
11.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
12.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
13.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
14.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
15.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001

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