Mixed Index Laws

Mixed Index Laws brings the multiplication, division, power of a power and zero index laws together in one expression in NSW Year 8 maths (NESA outcome MA4‑IND‑C‑01). The key is to apply one law at a time and write a line for each step, watching for a hidden index of 1.

You will simplify expressions such as \(\frac{(5^4)^2 \times 8^0}{5^6}\) and \((3^4)^3 \div 3^9 \times 3\), handle negative bases and two bases at once, and leave a fraction when the bottom power is larger. You will find hidden indices and finish with pronumeral expressions, a first look at Stage 5 work, like \((4x^3y)^2 \div (2xy)^3\). The volume of a cube-shaped box with edges of \(2^2 \times 5\) cm is one example. It is part of Year 8 Algebra.