Indices & Reciprocals - SS1 Mathematics Lesson Note

Indices or Powers

Given a number \(5^{4}\), which can be expanded as \(5 \times 5 \times 5 \times 5\). The number of places \(5\) must multiply itself is called the order or power or index (plural: indices) of \(5\), which in this case is \(4\). Generally, \(a^{b}\) means \(a\) multiplies itself \(b\) times.

Reciprocals

If the product of two numbers is \(1\), then the two numbers are said to be reciprocals of each other. If \((a)(b) = 1\), then \(b = \frac{1}{a}\), so \((a)(b) = (a)\left( \frac{1}{a} \right) = \ \frac{a}{1} \times \frac{1}{a} = 1\). For instance, \(5\ \)and\(\ \frac{1}{5}\) are reciprocals of each other, as their product is \(1\). Also, the reciprocal of \(\frac{5}{8}\) is \(\frac{8}{5}\) and the reciprocal of \(- \frac{1}{3}\) is \(- \frac{3}{1} = - 3\).

Another phrase for reciprocals is multiplicative inverse.