GCSE · Indices

The index lawsExam-style questions

Why multiplying powers adds the indices, dividing subtracts them, and a power of a power multiplies them — and why every part of a bracket, coefficient included, takes the power.

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

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Write $\dfrac{(2x^{3}y)^{4} \times 3xy^{5}}{6x^{7}y^{11}}$ in the form $ax^{b}y^{c}$ where $a$ , $b$ and $c$ are integers.

(3 marks)
Level 4 · 3 marksTry it
2
Write $8^2 \times 4^3$ as a single power of 2.
Level 4 · 3 marksTry it
3
$3^n \times 9^2 = 3^{11}$ . Work out the value of $n$ .
Level 4 · 3 marksTry it
4
Write $27^2 \times 9^2$ as a single power of $3$ .
Level 4 · 3 marksTry it
5
$\left(2^n\right)^3 \div 2^5 = 2^{16}$

Work out the value of $n$ .
Level 4 · 3 marksTry it