Answer
$-\displaystyle \frac{12y^{15}}{x^{3}}$
Work Step by Step
$\displaystyle \frac{24x^{2}y^{13}}{-2x^{5}y^{-2}}=\frac{24}{-2}\cdot\frac{x^{2}}{x^{5}}\cdot\frac{y^{13}}{y^{-2}}\quad$ ... use the rule:$\displaystyle \quad \frac{a^{m}}{a^{n}}=a^{m-n}$
$=-12x^{2-5}y^{13-(-2)}$
$=-12x^{-3}y^{15}\quad $... use the rule: $a^{-n}=\displaystyle \frac{1}{a^{n}}$
=$-\displaystyle \frac{12y^{15}}{x^{3}}$
