Rational Exponents: exemplo 9.104

We want to write each radical in the form $a^{\frac{1}{n}}$.

ⓐ
$\begin{array}{cccc}& & & \sqrt{x}\hfill \\ \begin{array}{c}\text{No index is shown, so it is 2.}\hfill \\ \text{The denominator of the exponent will be 2.}\hfill \end{array}\hfill & & & x^{\frac{1}{2}}\hfill \end{array}$

ⓑ
$\begin{array}{cccc}& & & \sqrt[3]{y}\hfill \\ \begin{array}{c}\text{The index is 3, so the denominator of the}\hfill \\ \text{exponent is 3.}\hfill \end{array}\hfill & & & y^{\frac{1}{3}}\hfill \end{array}$

ⓒ
$\begin{array}{cccc}& & & \sqrt[4]{z}\hfill \\ \begin{array}{c}\text{The index is 4, so the denominator of the}\hfill \\ \text{exponent is 4.}\hfill \end{array}\hfill & & & z^{\frac{1}{4}}\hfill \end{array}$