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

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1.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
2.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
3.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
4.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
5.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
6.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
7.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
8.Work out the value of 2⁻⁴
(a)16
(b)−16
(c)1/8
(d)1/16
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 $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
11.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶
12.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
(a)2¹²
(b)2¹
(c)4⁷
(d)2⁷
13.Work out the value of (√5)⁴
(a)25
(b)625
(c)20
(d)5
14.Work out the value of $2^{3} + 3^{2}$ .
(a)17
(b)72
(c)12
(d)−1
15.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾
(a)x
(b)x⁽³⁄¹⁶⁾
(c)x³
(d)x⁽¹⁄²⁾

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