Question

Simplify:√(729)^5/3=

Answer 1

Question -

({(729)}^{ \frac{ - 5}{3} } ) ^{ \frac{ - 1}{2} } = {(729)}^{ \frac{ - 5}{3} \times \frac{ - 1}{2} }

Answer -

LHS -

({(729)}^{ \frac{ - 5}{3} })^{ \frac{ - 1}{2} }

we \: know \: ({a}^{m} ) ^{n} = {a}^{mn}

(729) ^{ \frac{5}{6} }

729 = {3}^{6}

({3}^{6}) ^{ \frac{5}{6} }

{3}^{5} = 243

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RHS -

(729) ^{ \frac{ - 5}{3} \times \frac{ - 1}{2} }

(729) ^{ \frac{5}{6} }

729 = {3}^{6}

( {3}^{6} ) ^{ \frac{5}{6} }

{3}^{5} = 243

Hence :

Verified : LHS = RHS .

HOPE IT HELPS