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

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

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

$$3^{2n}\times 2^3=m$$$$27{\left(3^n\right)}^2=m$$$$\frac{27{\left(3^n\right)}^2}{27}=\frac{m}{27}$$$${\left(3^n\right)}^2=\frac{m}{27}$$$$\sqrt{{\left(3^n\right)}^2}=\sqrt{\frac{m}{27}}$$$$3^n=\sqrt{\frac{m}{27}}$$$$3^{-n}=\frac{\sqrt{27}}{\sqrt{m}}$$$$=\frac{3\sqrt{3m}}{m}$$$$whenm>0$$

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