Edexcel IGCSE Math B 1.C indices powers and roots

Practise indices questions by rewriting powers with common bases, applying index laws and simplifying algebraic powers before solving.

Exam points

Use index laws to simplify expressions with powers, roots and algebraic variables.
Rewrite exponential equations with common bases before solving for x clearly.
Apply zero, negative or fractional powers such as p⁰ or powers of q and r.

[Maximum number: 3]

$c=4\times10^{-8n}$ , where n is an integer.
Find an expression for $c^{-\frac12}$ in terms of n.
Give your answer in standard form.

$\frac{1}{(4\times10^{-8n})^{1/2}}=\frac{1}{2\times10^{-4n}}$

Equivalent form: $\frac12\times10^{4n}$ .

Final answer: $5\times10^{4n-1}$ .

M1 for a correct power/root method.
A1 for a correct form involving $10^{4n}$ .
A1 for $5\times10^{4n-1}$ .

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1.C Indices, powers and roots question 1