Zero Index

Any number except zero raised to the power 0 equals 1. In NSW Year 8 maths you see why by dividing a power by itself in two ways: \(4^3 \div 4^3 = 1\), and the division law also gives \(4^{3-3} = 4^0\) (NESA outcome MA4‑IND‑C‑01).

You will evaluate expressions such as \(5 \times 8^0 \times 6 \times 3^0\) and \((7 \times 4)^0 + 7 \times 4^0\), noticing that a zero index belongs only to the base it sits on. You will cancel equal powers in fractions, combine the zero index with the other laws and simplify terms like \(2m^0\), a first look at Stage 5 work. Place value uses it too, because the ones column is \(10^0\). It is part of Year 8 Algebra.