Root

Use law of square roots roots:

6423=6n \sqrt[3] {\sqrt[2] { \sqrt[4] { 6 }}} = \sqrt[n] { 6 }


Result

n =  24

Solution:

6423=63⋅2⋅4=624 n=24 \sqrt[3] {\sqrt[2] { \sqrt[4] { 6 }}} = \sqrt[3\cdot 2\cdot 4] { 6 } = \sqrt[24] { 6 } \ \\ n = 24

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