Question

how are exponents related to taking the root of a number?

Answer 1

They are related through the identity \[\Huge x^{\frac{1}{n}}=\sqrt[n]{x}\]

Answer 2

For instance, taking the cube root of 8 is the same as raising 8 to the one-third power


So


\[\Huge \sqrt[3]{8}=8^{\frac{1}{3}}\]