Question

.find the value of n.
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Answer 1

$\begin{gathered}\huge\mathbb\star\purple{Relevant}\:\huge\mathbb\pink{Answer}\star\\\\\end{gathered}$

$\frac{ {9}^{n} \times {3}^{2} \times {3}^{n} - ( {27)}^{n} }{ ({3 ^{3} )}^{5} \times {2}^{3} } = \frac{1}{27} \\ \\ = > \frac{ {3}^{2n} \times {3}^{2} \times {3}^{n} - {3}^{3n} }{ {3}^{15} \times {2}^{3} } = \frac{1}{ {3}^{3} } \\ \\ = > \frac{ {3}^{3n} \times 9 - {3}^{3n} }{ {3}^{15} \times 8} = \frac{1}{ {3}^{3} } \\ \\ = > \frac{ {3}^{3n} \times ( {9} - 1) }{8} = \frac{1}{ {3}^{3} } \times {3}^{15} \\ \\ = > \frac{ {3}^{n} \times 8}{8} = {3}^{(15 - 3)} \\ \\ = > {3}^{n} = {3}^{12} \\ \\ = > n = 12$

HOPE THIS HELPS YOU ☝️....