Sure! Let's solve the expression \(\sqrt[5]{\frac{8}{125}}\) step by step.
1. Identify the components of the expression:
- The numerator is \(8\).
- The denominator is \(125\).
- We are asked to find the fifth root of the fraction.
2. Rewrite the expression:
The expression \(\sqrt[5]{\frac{8}{125}}\) can be rewritten as \(\left(\frac{8}{125}\right)^{\frac{1}{5}}\).
3. Evaluate the fraction:
We need to first consider the fraction \(\frac{8}{125}\). The fraction \(8\) (numerator) divided by \(125\) (denominator) is retained as \(\frac{8}{125}\).
4. Apply the fifth root:
The fifth root of a number \(x\) is the same as raising \(x\) to the power of \(\frac{1}{5}\). Therefore, we need to compute \(\left(\frac{8}{125}\right)^{\frac{1}{5}}\).
After performing this calculation, we find that the result is approximately:
[tex]\[ \sqrt[5]{\frac{8}{125}} \approx 0.5770799623628854 \][/tex]
Thus, [tex]\(\sqrt[5]{\frac{8}{125}}\)[/tex] evaluates to [tex]\(0.5770799623628854\)[/tex].
