Question

Precalculus Evaluate 32^-3/5

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^{-(3)/(5)}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5 \end{cases}\implies (2^5)^{-(3)/(5)}\implies 2^{-(3)/(5)\cdot 5} \\\\\\ 2^(-3)\implies \cfrac{1}{2^3}\implies \cfrac{1}{8}`