Question

What is the value of the following radical expression?

Answer 1

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

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

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

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

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

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

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

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

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

{ Pisces04 }

Answer 2

b.) 2

Step-by-step 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`