Question

$5\sqrt[4]{\sqrt[3]{5}} - \sqrt[3]{\sqrt[4]{5} }$?

Answer 1

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$\red{5 \sqrt[4]{ \sqrt[3]{5} } - \sqrt[3]{ \sqrt[4]{5} } } = \purple{5 {( ({5)}^{ \frac{1}{3} } )}^{ \frac{1}{4} } - {(( {5)}^{ \frac{1}{4} }}^{ \frac{1}{3} } )}$

$\red{{5 {( ({5)}^{ \frac{1}{3} } )}^{ \frac{1}{4} } - {(( {5)}^{ \frac{1}{4} }}^{ \frac{1}{3} } )}} = \purple{5 {(5)}^{ \frac{1}{12} } - {(5)}^{ \frac{1}{12} } }$

$\red{5 {(5)}^{ \frac{1}{12} } - {(5)}^{ \frac{1}{12} } } = \purple{ {5}^{ \frac{1}{12} } (5 - 1)}$

$\red{ {5}^{ \frac{1}{12} }(5 - 1) } = \purple{4 {(5)}^{ \frac{1}{12} } }$

Answer 2

Step-by-step explanation:

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