Find Value of Given Expression

Question

\[ \{5(8^{1/3}+27^{1/3})^3\}^{1/4} \]

Solution

\[ 8^{1/3} = 2,\quad 27^{1/3} = 3 \]
\[ = \{5(2+3)^3\}^{1/4} \]
\[ = \{5 \cdot 5^3\}^{1/4} \]
\[ = \{5^4\}^{1/4} \]
\[ = 5 \]

Answer

\[ \boxed{5} \]

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