## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-\displaystyle \frac{12b^{26}}{7a^{12}}$
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 $a^{-n}=\displaystyle \frac{1}{a^{n}}$ $=-\displaystyle \frac{12}{7}\times\frac{1}{a^{12}}\times b^{26}$ $=-\displaystyle \frac{12b^{26}}{7a^{12}}$