Let's evaluate the expression step-by-step.
The given expression is:
[tex]\[
\frac{-7}{2 \sqrt[5]{3^2}}
\][/tex]
First, evaluate the term inside the root:
[tex]\[
3^2 = 9
\][/tex]
Now, we need to find the fifth root of 9. Let's denote this as [tex]\(9^{1/5}\)[/tex]. So we have:
[tex]\[
\sqrt[5]{9} = 9^{1/5} \approx 1.5518455739153598
\][/tex]
Next, multiply this result by 2:
[tex]\[
2 \times 9^{1/5} \approx 2 \times 1.5518455739153598 = 3.1036911478307196
\][/tex]
Now, we divide the numerator by this result:
[tex]\[
\frac{-7}{3.1036911478307196} \approx -2.25537905242039
\][/tex]
So the final answer to the expression is:
[tex]\[
\frac{-7}{2 \sqrt[5]{3^2}} \approx -2.25537905242039
\][/tex]
