Power of a Power

To raise a power to another power, keep the base and multiply the indices: \((a^m)^n = a^{mn}\). In NSW Year 8 maths this sits alongside the power of a product, where every factor inside the bracket is raised to the outside index (NESA outcome MA4‑IND‑C‑01).

You will simplify expressions such as \((3^2)^4\) and \((3 \times 2^4)^2\), deal with negative bases like \(((-2)^3)^3\), write \(25^4\) as a power of 5 and work backwards to a missing index. You will also extend the law to pronumerals, a first look at Stage 5 work, in \((3x^2y)^4\). The number of square metres in a square kilometre and the small cubes in a large cube are found with this law. It is part of Year 8 Algebra.