Question

What is the value of the following radical expression?

Answer 1

$\large\displaystyle\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered} }$

$\large\displaystyle\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered} }$

$\large\displaystyle\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$

$\large\displaystyle\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$

$\large\displaystyle\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$

{ Pisces04 }

Answer 2

Answer:

b.) 2

Explanation:

Given:

• $\sf - \sqrt[\sf 5]{\sf -32}$

rewrite knowing 2⁵ = 32, (-2)⁵  = -32

• $\sf -\left(\sqrt[5]{(-2)^5}\right)$

simplify, ⁿ√xⁿ = x

• $\sf -\left(-2}\right)$

distribute inside parenthesis

• $\sf 2$