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.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
2.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
3.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
4.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
5.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶
6.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
7.Work out the value of ∛125.
(a)5
(b)375
(c)15625
(d)62.5
8.Write down the value of 3⁰
(a)3
(b)0
(c)1/3
(d)1
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 √64.
(a)16
(b)4
(c)32
(d)8
11.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
12.Write down the value of 7⁰
(a)1/7
(b)1
(c)7
(d)0
13.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
14.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
15.Work out the value of 5³.
(a)8
(b)53
(c)125
(d)15

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