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 Higher

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

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 x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
2.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾
(a)x
(b)x⁽³⁄¹⁶⁾
(c)x³
(d)x⁽¹⁄²⁾
3.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
4.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
5.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
6.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
7.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
8.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
9.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
10.Work out the value of $2^{3} + 3^{2}$ .
(a)17
(b)72
(c)12
(d)−1
11.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
12.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
13.Simplify (3a²)² × (2a)³
(a)17a⁷
(b)72a¹²
(c)36a⁷
(d)72a⁷
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

Build your own mix at the worksheet builder.