Question

How do i do this ？ please not just the answer

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 32^{-\frac{2}{5}}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5 \end{cases}\implies (2^5)^{-\frac{2}{5}}\implies 2^{-\frac{2}{5}\cdot 5}\implies 2^{-2} \\\\\\ \cfrac{1}{2^2}\implies \cfrac{1}{4}$