Indices are also known as powers or orders. Note that indices is plural and index is singular. It can be shown that indices abide by the following rules in maths:

The Laws of Indices

  • x^a\times x^b=x^{a+b}
  • x^a\div x^b=x^{a-b}
  • \left(x^a\right)^b=x^{ab}
  • x^{-n}=\frac{1}{x^n}
  • x^{\frac{m}{n}}=\left(\sqrt[n]{x}\right)^m

Example 1

2^7\times 2^9=2^{16}

Example 2


Example 3


Example 4

16\times 2^{-3}=16\times \frac{1}{2^3}=16\times \frac{1}{8}=2

Example 5