Printable · GCSE Foundation · ages 14-16

Calculating with roots and indices worksheet — GCSE Foundation

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 Foundation

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

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1.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
2.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
3.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
4.Write down the value of 7⁰
(a)1/7
(b)1
(c)7
(d)0
5.Work out the value of ∛8.
(a)24
(b)2
(c)4
(d)64
6.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
7.Simplify x⁷ × x⁴, giving your answer as a single power of x.
(a)x¹¹
(b)11x
(c)x³
(d)x²⁸
8.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
9.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
10.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
11.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
12.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
13.Work out the value of ∛125.
(a)5
(b)375
(c)15625
(d)62.5
14.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
15.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶

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