Question

Simplify:
$\frac{ {3}^{2n + 4} - {5.3}^{2(n + 1)} }{ {(9)}^{n - 1} }$
​

Answer 1

${\huge {\red {\mid{ \fbox{ \tt{Question}} \mid}}}}$

Simplify:

$\frac{ {3}^{2n + 4} - {5.3}^{2(n + 1)} }{ {(9)}^{n - 1} }$

${\huge {\red {\mid{ \fbox{ \tt{Solution}} \mid}}}}$

$\frac{ {3}^{2n + 4} - {5.3}^{2(n + 1)} }{ {(9)}^{n - 1} }$

$= \frac{ {3}^{2n}. {3}^{4} - {5.3}^{2n} . {3}^{2} }{ {({3}^{2}) }^{n - 1} }$

$= \frac{ {3}^{2n} .81 - {3}^{2n}.45 }{ {3}^{2n} . {3}^{ - 2} }$

$= \frac{ {3}^{2n}.(81 - 45) \times {3}^{2} }{ {3}^{2n} }$

$= 36 \times 9 = \bf{324}$