if-3-2n-3-m-find-3-n-

Question Number 21100 by ibraheem160 last updated on 12/Sep/17

if 3^{2 n + 3} = m, find 3^{- n}

Commented by chernoaguero@gmail.com last updated on 13/Sep/17

3^{2 n} \times 2^{3} = m

27 {(3^{n})}^{2} = m

\frac{27 {(3^{n})}^{2}}{27} = \frac{m}{27}

{(3^{n})}^{2} = \frac{m}{27}

\sqrt{{(3^{n})}^{2}} = \sqrt{\frac{m}{27}}

3^{n} = \sqrt{\frac{m}{27}}

3^{- n} = \frac{\sqrt{27}}{\sqrt{m}}

= \frac{3 \sqrt{3 m}}{m}

w h e n m > 0