Question

How do i simplify this

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \cfrac{3^4}{3^6} \right)^2\implies \left( \cfrac{3^(4\cdot 2)}{3^(6\cdot 2)} \right)\implies \cfrac{3^8}{3^(12)}\implies \cfrac{1}{3^(12)\cdot 3^(-8)}\implies \cfrac{1}{3^(12-8)}\implies \cfrac{1}{3^4}\implies \cfrac{1}{81}`