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.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
2.Simplify x⁷ × x⁴, giving your answer as a single power of x.
(a)x¹¹
(b)11x
(c)x³
(d)x²⁸
3.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
4.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
5.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
6.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
7.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
8.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
9.Simplify (3a²)² × (2a)³
(a)17a⁷
(b)72a¹²
(c)36a⁷
(d)72a⁷
10.Work out the value of $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
11.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
12.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶
13.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
14.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
15.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4

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