Answer
$-\displaystyle \frac{12b^{26}}{7a^{12}}$
Work Step by Step
Gather like terms
$\displaystyle \frac{24a^{-1}b^{10}}{-14a^{11}b^{-16}}=\frac{24}{-14}\times\frac{a^{-1}}{a^{11}}\times\frac{b^{10}}{b^{-16}}$
... reduce the numerical fraction by 2,
... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=-\displaystyle \frac{12}{7}\times a^{-1-11}\times b^{10-(-16)}$
$=-\displaystyle \frac{12}{7}\times a^{-12}\times b^{26}$
... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$
$=-\displaystyle \frac{12}{7}\times\frac{1}{a^{12}}\times b^{26}$
$=-\displaystyle \frac{12b^{26}}{7a^{12}}$
