# How do you simplify  ((8x^3 )/ (27y^6))^(1/3)?

May 1, 2017

$\frac{2 x}{3 {y}^{2}}$
${\left(\frac{8 {x}^{3}}{27 {y}^{6}}\right)}^{\frac{1}{3}}$ is the same as ${\left(\frac{\textcolor{g r e e n}{{2}^{3}} {x}^{3}}{\textcolor{g r e e n}{{3}^{3}} {y}^{6}}\right)}^{\frac{1}{3}}$
Distribute the external exponent $\left(\textcolor{red}{\frac{1}{3}}\right)$into the exponents inside (for both numerator and the denominator)
${\left(\frac{\textcolor{g r e e n}{{2}^{3}} {x}^{3}}{\textcolor{g r e e n}{{3}^{3}} {y}^{6}}\right)}^{\textcolor{red}{\frac{1}{3}}} = \frac{\textcolor{g r e e n}{{2}^{3 \cdot \textcolor{red}{\frac{1}{3}}}} {x}^{3 \cdot \textcolor{red}{\frac{1}{3}}}}{\textcolor{g r e e n}{{3}^{3 \cdot \textcolor{red}{\frac{1}{3}}}} {y}^{6 \cdot \textcolor{red}{\frac{1}{3}}}} = \frac{\textcolor{g r e e n}{2} x}{\textcolor{g r e e n}{3} {y}^{2}}$