Following are the complete solution to the given expression:
Given:
[tex]\to \bold{(\sqrt[3]{2^5})^{\frac{1}{4}}}[/tex]
To find:
value=?
Solution:
[tex]\to \bold{(\sqrt[3]{2^5})^{\frac{1}{4}}}[/tex]
Using formula:
[tex]\therefore \\\\\to\bold{\sqrt[n]{a}=a^{\frac{1}{n}}}\\\\\to\bold{(a^m)^n=a^{m \cdot n}}\\\\[/tex]
[tex]\to (\sqrt[3]{2^5})^{\frac{1}{4}}\\\\\to [(2^{5})^{\frac{1}{3}}]^{\frac{1}{4}}\\\\\to 2^{5}\times \frac{1}{3}\times \frac{1}{4}\\\\\to 2^\frac{5}{12}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{2^{\frac{5}{12}}}[/tex]".
Note:
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