Power and Roots

Power and Roots in NSW Year 8 maths widens the base of a power to decimals, fractions and negative numbers, and takes roots of decimals (NESA outcome MA4‑IND‑C‑01). Brackets matter: \((-3)^2 = 9\) but \(-3^2 = -9\), and \(\left(\frac{3}{4}\right)^2 = \frac{9}{16}\).

You will evaluate powers such as \(0.3^2\) and \(\left(\frac{2}{3}\right)^3\), roots like \(\sqrt{1.44}\) and \(\sqrt[3]{0.027}\), and use \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\). You will apply the order of operations, find a missing number and spot last-digit patterns. The side of a square courtyard, the edge of a cube-shaped water tank and a chain message all involve powers and roots. It is part of Year 8 Working with Numbers.