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.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
2.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
3.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
4.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
5.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
6.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
7.Work out the value of $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
8.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
9.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
10.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
11.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
12.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
13.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶
14.Simplify x⁷ × x⁴, giving your answer as a single power of x.
(a)x¹¹
(b)11x
(c)x³
(d)x²⁸
15.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16

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