GCSE · Indices

Fractional indicesExam-style questions

Why a power of 1/n is an nth root, how m/n means "root, then power", how negative fractional indices chain reciprocal + root + power, and how to solve equations by matching bases.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
$5^{x} = 25^{n} \times \sqrt{5}$

$5^{y} = \dfrac{125^{n+1}}{\sqrt{5}}$

$y$ is $6$ more than $x$ .

Work out the value of $n$ .

(3 marks)
Level 5 · 3 marksTry it
2
Write $\left(16x^8\right)^{3/4}$ in the form $ax^n$ .
Level 5 · 3 marksTry it
3
Solve $2^{x+1} = 8^{x-1}$ .
Level 5 · 3 marksTry it
4
Write $\left(25x^6\right)^{3/2}$ in the form $ax^n$ .
Level 5 · 3 marksTry it
5
Solve $9^x = 27^{x-2}$
Level 5 · 3 marksTry it