itomath.com

Rational Exponents Part 2

$8^\frac{2}{3}$
$=$
$\left(8^2\right)$
$=$
$^\frac{1}{3}$
$=$
Or $\quad 8^\frac{2}{3}$
$=$
$\left(8^\frac{1}{3}\right)$
$=$
$^2$
$=$
$25^\frac{3}{2}$
$=$
$\left(25^3\right)$
$=$
$^\frac{1}{2}$
$=$
Or $\quad 25^\frac{3}{2}$
$=$
$\left(25^\frac{1}{2}\right)$
$=$
$^3$
$=$
$27^{-\frac{4}{3}}$
$=$
$\left(27^4\right)$
$=$
$^{-\frac{1}{3}}$
$=$
Or $\quad 27^{-\frac{4}{3}}$
$=$
$\left(27^\frac{1}{3}\right)$
$=$
$^{-4}$
$=$

Evaluate. Give your answers as fractions.

$27^{\frac{2}{3}}$
$\left(-27\right)^{\frac{2}{3}}$
$729^{-\frac{2}{3}}$
$\left(-1000\right)^{-\frac{2}{3}}$

$\left(\frac{1}{32}\right)^{\frac{2}{5}}$
$\left(-\frac{1}{343}\right)^{\frac{2}{3}}$
$\left(\frac{1}{729}\right)^{-\frac{2}{3}}$
$\left(-\frac{1}{512}\right)^{-\frac{2}{3}}$

$\left(\frac{8}{125}\right)^{\frac{4}{3}}$
$\left(-\frac{125}{64}\right)^{\frac{4}{3}}$
$\left(\frac{216}{343}\right)^{-\frac{2}{3}}$
$\left(-\frac{125}{729}\right)^{-\frac{2}{3}}$