Index laws

The index laws are shortcuts for combining powers of the same base without working out their values. In NSW Year 8 maths you use the multiplication law \(a^m \times a^n = a^{m+n}\) and the division law \(a^m \div a^n = a^{m-n}\) with numerical bases (NESA outcome MA4‑IND‑C‑01).

You will first write powers in expanded form to see why the laws work, then simplify products and quotients such as \(3^6 \times 3^2 \div 3^4\), find a missing index and rewrite bases like 16 and 64 as powers of 2. You will also check claims made by other students. Photo file sizes sent from a phone and computer memory are counted in powers of 2. It is part of Year 8 Working with Numbers.