Question

Someone please help ​

Answer 1

Answer:

$\large{ \green { \rm \: SOLUTION : - }}$

$\sf \large \bigg \{ \frac{ \big( {9}^{n + \frac{1}{4} } \big) \sqrt{3. {3}^{n} } }{3 \sqrt{ {3}^{ - n} } } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ \frac{ \big( {3}^{2(n + \frac{1}{4}) } \big) \sqrt{ {3}^{n + 1} } }{3.3 ^{ (\frac{ - n}{2}) } } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ \frac{ \big( {3}^{(2n + \frac{1}{2}) } \big) {3}^{ \frac{n + 1}{2} } }{3 ^{ (\frac{ - n}{2} + 1 )} } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ {3}^{(2n + \frac{1}{2} + \frac{n + 1}{2} - (\frac{ - n}{2} + 1) } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ {3}^{(2n + \frac{n}{2} + \frac{n}{2} + \frac{1}{2} + \frac{1}{2} - 1 } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ {3}^{(2n +n + \cancel1- \cancel1 } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ {3}^{(3n) } \bigg \}^{ \frac{1}{n} }$

$= \sf \large \bigg \{ {3}^{( \frac{3n}{n} ) } \bigg \}$

$\sf \: = {3}^{3}$

$\sf \: = 27$

$\sf \: Hence \: \: \boxed{ \large \: \tt\green A \blue n \pink{s} \orange{w} \gray{e} \red{r} \: \green{ is \: 27}}$