An example of a fractional index is \(g^{\frac{1}{3}}\). The denominatorThe bottom part of a fraction. For 鈪, the denominator is 8, which represents 'eighths'. of the fraction is the rootThe root of an equation is the same as the solution to the equation. of the number or letter, and the numeratorThe top part of a fraction. For 鈪 , the numerator is 5. of the fraction is the power to raise the answer to.
\(a^{\frac{1}{2}} = \sqrt{a}\), \(a^{\frac{1}{3}} = \sqrt[3]{a}\) and so on.
By using index laws for multiplication from earlier it is clear to see that:
\(g^{\frac{1}{2}} \times g^{\frac{1}{2}} = g^1\)
Therefore: \(g^{\frac{1}{2}} = \sqrt{g}\)
\(a^{\frac{m}{n}} = (\sqrt[n]{a})^m\)
Question
Simplify \(t^{\frac{3}{2}}\).
Simplify \(8^{\frac{2}{3}}\).
\(a^{\frac{m}{n}} = (\sqrt[n]{a})^m\), so \(t^{\frac{3}{2}} = (\sqrt[2]{t})^3\)