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.

\(8\frac{1}{3} = 2\)

\(a^{\frac{m}{n}} = (\sqrt[n]{a})^m\)

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

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