Calculate: cube root of-125/27

Expression: $\sqrt[3]{-\frac{125}{27}}$

Apply radical rule $\sqrt[n]{-a}=-\sqrt[n]{a}, $if $n$ is odd

$=-\sqrt[3]{\frac{125}{27}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\quad$ assuming $a\ge0, b\ge0$

$=-\frac{\sqrt[3]{125}}{\sqrt[3]{27}}$

$\sqrt[3]{27}=3$

$=-\frac{\sqrt[3]{125}}{3}$

$\sqrt[3]{125}=5$

$=-\frac{5}{3}$