GCSE · Indices

Zero and negative indicesExam-style questions

Why anything to the power zero is 1 (not 0), why a negative index means a reciprocal (not a negative number), and why a fraction raised to a negative power flips.

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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
For $x \neq 0$ , the expression $5x^{-2}(2x^{2} - 3x^{7})$ can be written as $a + bx^{n}$

Find the value of $a$ , the value of $b$ and the value of $n$ .

(2 marks)
Level 4 · 2 marksTry it
2
Evaluate $\left(\dfrac{2}{5}\right)^{-3}$ . Give your answer as a fraction.
Level 4 · 2 marksTry it
3
Write $\dfrac{6x^2}{2x^{-3}}$ in the form $ax^n$ .
Level 4 · 2 marksTry it
4
$5^{2x} \times 5^{-3} = 5^{7}$ . Work out the value of $x$ .
Level 4 · 2 marksTry it
5
Evaluate $\left(\dfrac{3}{4}\right)^{-2}$ . Give your answer as a fraction.
Level 4 · 2 marksTry it

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