Answer
$\frac{a^{12}b^{30}}{c^{66}}$
Work Step by Step
We are given the expression $(\frac{a^{-2}b^{-5}}{c^{-11}})^{-6}$.
To simplify, we can use the power of a quotient rule, which holds that $(\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}$, $b\ne0$ (where a and b are real numbers, and n is an integer).
$(\frac{a^{-2}b^{-5}}{c^{-11}})^{-6}=\frac{(a^{-2}b^{-5})^{-6}}{(c^{-11})^{-6}}$
To simplify further, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers).
$\frac{(a^{-2}b^{-5})^{-6}}{(c^{-11})^{-6}}=\frac{a^{12}b^{30}}{c^{66}}$
