Indices are a way of representing numbers and letters that have been multiplied by themselves a number of times. They help us to complete problems involving powers more easily.
Part ofMathsNumber
The denominator is the root.
The numerator is the power.
\({a}^\frac{1}{2}\)
Therefore, \({a}^\frac{1}{2} = (\sqrt{a})^{1}\)
\({8}^\frac{2}{3}\) = \((\sqrt[3]{8})^{2}\)
= 22
= 4
Therefore, \({a}^\frac{n}{m} = (\sqrt[m]{a})^{n} = \sqrt[m]({a}^{n})\)
Evaluate \({16}^\frac{1}{2}\)
\({16}^\frac{1}{2} = (\sqrt{16})\)
Evaluate \({27}^\frac{2}{3}\)
\({27}^\frac{2}{3} = (\sqrt[3]{27})^{2}\)
= 32
= 9
\({a}^{n} \times {a}^{m} = {a}^{n+m}\)
\({a}^{n} ÷ {a}^{m} = {a}^{n-m}\)
\(({a}^{n})^{m} = {a}^{n \times m}\)
\({a}^{0} = {1}\)
\({a}^{-n} = \frac{1}{a^n}\)
\({a}^\frac{n}{m} = (\sqrt[m]{a})^{n} = \sqrt[m]({a}^{n})\)
