# Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 12

$\frac{a^{12}b^{30}}{c^{66}}$

#### 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). $\frac{(a^{-2}b^{-5})^{-6}}{(c^{-11})^{-6}}=\frac{a^{12}b^{30}}{c^{66}}$

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