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.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
2.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
3.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
4.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
5.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
6.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
7.Work out the value of $2^{3} + 3^{2}$ .
(a)17
(b)72
(c)12
(d)−1
8.Simplify (3a²)² × (2a)³
(a)17a⁷
(b)72a¹²
(c)36a⁷
(d)72a⁷
9.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
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.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶
12.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾
(a)x
(b)x⁽³⁄¹⁶⁾
(c)x³
(d)x⁽¹⁄²⁾
13.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
14.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
15.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹

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