Further Index laws

Further Index Laws adds two more rules in NSW Year 8 maths (NESA outcome MA4‑IND‑C‑01). A power of a power multiplies the indices, \((a^m)^n = a^{mn}\), and any non-zero number to the power zero equals 1, as the pattern \(3^2 = 9\), \(3^1 = 3\), \(3^0 = 1\) shows.

You will simplify expressions like \((7^3)^5\) and \((4^5)^2 \div 4^7\), evaluate zero powers such as \(56 + 56^0\), and use \((6 \times 5)^2 = 6^2 \times 5^2\) as a shortcut. You will find missing indices, write \(9^5\) as a power of 3 and decide whether \(2^{30}\) or \(3^{20}\) is larger without a calculator. The area of a square paddock and the volume of a storage box can be written as powers. It is part of Year 8 Working with Numbers.