Indices Questions with Solutions

Indices, also called exponents or powers, show how many times a number is multiplied by itself. This topic covers the laws of indices: a^m x a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1, negative indices (a^-n = 1/a^n), and fractional indices (a^(1/n) is the nth root of a). It also covers surds and solving exponential equations. The standard approach for exponential equations is to write both sides with the same base and then equate the powers. For example, 4^x = 32 becomes 2^(2x) = 2^5, so x = 5/2. Comparing large powers is often easiest after rewriting them with a common exponent. Practise the indices questions below, each with a step-by-step solution showing which law of indices is used.