An example of a fractional index is \(g^{\frac{1}{3}}\). The denominator of the fraction is the root of the number or letter, and the numerator of the fraction is the power to raise the answer to.

\(g^{\frac{1}{2}} \times g^{\frac{1}{2}} = g^1\)

Therefore: \(g^{\frac{1}{2}} = \sqrt{g}\)

In general, \(a^{\frac{1}{2}} = \sqrt{a}\), \(a^{\frac{1}{3}} = \sqrt[3]{a}\) and so on.

\(8^{\frac{1}{3}} = \sqrt[3]{8} = 2\)

It is possible to combine fractional indices with raising a power to a power \(a^{\frac{m}{n}} = (\sqrt[n]{a})^m\).

Simplify \(27^{\frac{-2}{3}}\).

\(27^{\frac{-2}{3}}=(\sqrt[3]{27}){^{-2}}=3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}\)