Raising a power to a power

Check out the updated revision resources for GCSE Maths: Raising a power to a power, with step-by-step slideshows, quizzes, practice exam questions, and more!

Example

\((k^3)^2\).

This means that \(k^3\) is to be squared, or multiplied by \(k^3\) again: \((k^3)^2 = k^3 \times k^3\)

Add the powers together, so \((k^3)^2 = k^3 \times k^3 = k^6\), so \((k^3)^2\) can be simplified to \(k^6\).

Example

\((p^4)^3 = p^{4×3} = p^{12}\)

Example - Higher

Simplify \((2p^4)^3\)

Deal with the number and the letter separately.

\((2)^3 = 8\)

\((p^4)^3 = p^{4×3} = p^{12}\)

So \((2p^4)^3 = 8p^{12}\)

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Laws of indices - OCRRaising a power to a power