Question

Simplify $\frac{-10a^2b^4}{5a^{-9}b^{-5}}$

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ \cfrac{-10a^2b^4}{5a^{-9}b^{-5}}\implies \cfrac{-10}{5}\cdot \cfrac{a^2b^4}{a^{-9}b^{-5}}\implies \cfrac{-2}{1}\cdot \cfrac{a^2a^9b^4b^5}{1} \\\\\\ -2a^{2+9}b^{4+5}\implies -2a^{11}b^9$