Question

Can someone give me steps on how to do this??

`exponent`

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)} \\\\ -------------------------------`


`\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)}`