[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]
{ Pisces04 }
