Question

solve urgently . relevant answers only ​

Answer 1

Answer:

$\frac{ {9}^{n} \times {3}^{2} \times { {3}^{ \frac{ - n}{2} } }^{ - 2} - {27}^{n} }{ {3}^{3m} \times {2}^{3} } = \frac{1}{729} \\ \frac{ {3}^{2n } \times {3}^{2} \times {3}^{n} - {3}^{3n} }{{3}^{3m} \times {2}^{3} } = \frac{1}{ {9}^{3} } \\ \frac{ {3}^{2n + 2 + n} - {3}^{3n} }{ {3}^{3m} \times {2}^{3} } = \frac{1}{ {( {3}^{2}) }^{3} } \\ \frac{ {3}^{3n + 2} - {3}^{3n} }{ {3}^{3m} \times {2}^{3} } = \frac{1}{ {3}^{6} } \\ \frac{ {3}^{3n} ( {3}^{2} - 1) }{ {3}^{3m} \times 8} = \frac{1}{ {3}^{6} } \\ = \frac{{3}^{3n} \times 8}{ {3}^{3m} \times 8} = {3}^{ - 6} \\ {3}^{3n - 3m} = {3}^{ - 6} \\ 3n - 3m = - 6 \\ n - m = - 2 \\ m - n = 2$