[tex]\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}}
\\\\
-------------------------------[/tex]
[tex]\bf \cfrac{2(3a^4b^{-2}c^{-2})^{-2}}{3a^2b^2c^2}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{2(3^{-2}a^{-2\cdot 4}b^{-2\cdot -2}c^{-2\cdot -2})}{3a^2b^2c^2}}
\\\\\\
\cfrac{2(3^{-2}a^{-8}b^4c^4)}{3a^2b^2c^2}\implies 2\cdot \cfrac{1}{3^2}\cdot \cfrac{a^{-8}b^4c^4}{3a^2b^2c^2}\implies 2\cdot \cfrac{1}{9}\cdot \cfrac{b^4b^{-2}c^4c^{-2}}{3a^2a^8}
\\\\\\
\cfrac{2}{9}\cdot \cfrac{b^{4-2}c^{4-2}}{3a^{2+8}}\implies \cfrac{2}{9}\cdot \cfrac{b^2c^2}{3a^{10}}\implies \cfrac{2b^2c^2}{27a^{10}}[/tex]
