Question

# 9" x 32 x (31/2-(27)" 33m x 23 1 17. If prove that m-n=1.

Solution

$\frac{{9}^{n}\times {3}^{2}\times {\left({3}^{-n/2}\right)}^{-2}-{\left(27\right)}^{n}}{{3}^{3m}\times {2}^{3}}=\frac{1}{27}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{{\left({3}^{2}\right)}^{n}\times {3}^{2}\times \left({3}^{n}\right)-{(3}^{}}{}$