Sometimes writing Roots as Exponents, or vice versa, can be a bit tricky if we see something like the examples below.

Examples

$$\sqrt{ab} = (ab)^{\frac{1}{2}} = a^{\frac{1}{2}}b^{\frac{1}{2}}$$

$$\sqrt[3]{a^2} = a^{\frac{2}{3}}$$

$$\sqrt[5]{x^3} = x^{\frac{3}{5}}$$

$$\sqrt[3]{x^9} = x^{\frac{9}{3}} = x^3$$

$$\sqrt[4]{x^4} = {(x^4)}^{1/4} = {|x|}^{\frac{4}{4}} = |x|$$

Note that the exponent under the radical (the square root thingy) becomes the numerator of the fraction and the number on top of the radical becomes the denominator.