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
(a) Simplify $(2a^3b)^4$ (2 marks)
(b) Work out the value of $8^{\frac{2}{3}}$ (1 mark)
Level 3 · 3 marksTry it
2
Simplify:

(a) $x^5 \times x^3$

(b) $y^9 \div y^3$

(c) $(z^4)^3$
Level 3 · 3 marksTry it
3
Simplify $(3x^2y)^3$ .
Level 3 · 2 marksTry it
4
Simplify:

(a) $3a^2 \times 4a^5$

(b) $20b^8 \div 4b^2$
Level 3 · 4 marksTry it
5
Simplify $\left(2x^3y^2\right)^4$
Level 3 · 2 marksTry it