Question

Simplify:-
$\sqrt[5]{ \sqrt[4]{( {2}^{4}) {}^{3} } } - 5 \sqrt[5]{8} + 2 \sqrt[5]{ \sqrt[4]{( {2}^{3}) ^{3} } }$
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Answer 1

$2^{\frac{29}{20}}+2-5\times 2^{\frac{3}{5}}\approx -2.846502319$

Answer 2

$\huge \dag \: { \boxed{ \underline{ \purple{ \sf{Answer}}}}}$

$\sqrt[5]{ \sqrt[4]{( {2}^{4}) {}^{3} } } - 5 \sqrt[5]{8} + 2 \sqrt[5]{ \sqrt[4]{( {2}^{3}) ^{3} } }$

$\rightarrow \sqrt[5]{ \sqrt[4]{4096} } - 5 \sqrt[5]{8} + 2 \sqrt[5]{ \sqrt[4]{4096} }$

$\rightarrow \: \sqrt[5]{8} - 5 \sqrt[5]{8} + 3 \sqrt[5]{8}$

$\rightarrow \: - 5 \sqrt[5]{8} \: + \: 3 \sqrt[5]{8}$

$\rightarrow - 2 \sqrt[5]{8}$