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Rational Exponents

$^2$
$=$
$9$
$\displaystyle \left(\textcolor{red}{9^{\frac{1}{2}}}\right)^2$
$=$
$9$
Therefore, $\displaystyle \textcolor{red}{9^{\frac{1}{2}}}$
$=$
$^2$
$=$
$7$
$\displaystyle \left(\textcolor{red}{7^{\frac{1}{2}}}\right)^2$
$=$
$7$
Therefore, $\displaystyle \textcolor{red}{7^{\frac{1}{2}}}$
$=$
$^3$
$=$
$8$
$\displaystyle \left(\textcolor{red}{8^{\frac{1}{3}}}\right)^3$
$=$
$8$
Therefore, $\displaystyle \textcolor{red}{8^{\frac{1}{3}}}$
$=$
$^3$
$=$
$10$
$\displaystyle \left(\textcolor{red}{10^{\frac{1}{3}}}\right)^3$
$=$
$10$
Therefore, $\displaystyle \textcolor{red}{10^{\frac{1}{3}}}$
$=$

In general,
$a^\frac{1}{2}=\boxed{\;\sqrt{a}\;}$
$a^\frac{1}{3}=$
$a^\frac{1}{4}=$
$a^\frac{1}{n}=$

Evaluate. Give your answers as fractions.

$216^{\frac{1}{3}}$
$8^{\frac{1}{3}}$
$\left(-1000\right)^{\frac{1}{3}}$
$\left(-125\right)^{\frac{1}{3}}$

$343^{-\frac{1}{3}}$
$49^{-\frac{1}{2}}$
$\left(-1000\right)^{-\frac{1}{3}}$
$\left(-125\right)^{-\frac{1}{3}}$

Evaluate. Give your answers as fractions.

$4^{\frac{1}{2}}$
$\left(-512\right)^{-\frac{1}{3}}$
$25^{\frac{1}{2}}$
$729^{-\frac{1}{3}}$

$\left(-8\right)^{\frac{1}{3}}$
$81^{-\frac{1}{4}}$
$32^{\frac{1}{5}}$
$\left(-32\right)^{-\frac{1}{5}}$

$\left(-512\right)^{\frac{1}{3}}$
$125^{\frac{1}{3}}$
$\left(-27\right)^{-\frac{1}{3}}$
$\left(-1000\right)^{-\frac{1}{3}}$

$\left(-729\right)^{\frac{1}{3}}$
$1000^{-\frac{1}{3}}$
$\left(-27\right)^{\frac{1}{3}}$
$64^{-\frac{1}{6}}$