Index Laws for Multiplying and Dividing

Powers of the same base are multiplied by adding the indices and divided by subtracting them. In NSW Year 8 maths these laws are used in products such as \((5 \times 2^6) \times (3 \times 2^4)\), where the numbers in front are handled separately from the powers (NESA outcome MA4‑IND‑C‑01).

You will simplify products and quotients with one or two bases and negative numbers in front, leave a fraction where needed, find hidden numbers and indices, and use \(2 \times 5 = 10\) to evaluate. You will also take a first look at the same laws with pronumerals, which is Stage 5 work, as in \(\frac{48a^{10}b^6}{16a^5b^2}\). Working out how many days a city reservoir would last uses powers of 10. It is part of Year 8 Algebra.