Answer
$\frac{c^{18}}{64a^{12}b^{6}}$
Work Step by Step
We are given the expression $(2a^{2}bc^{-3})^{-6}$.
To simplify, 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).
$(2a^{2}bc^{-3})^{-6}=(2^{-6})\times(a^{2\times-6})\times(b^{1\times-6})\times(c^{-3\times-6})=$
$(2^{-6})\times(a^{-12})\times(b^{-6})\times(c^{18})=\frac{c^{18}}{2^{6}a^{12}b^{6}}=\frac{c^{18}}{64a^{12}b^{6}}$
