Question Number 21100 by ibraheem160 last updated on 12/Sep/17
$$\mathrm{if}\:\mathrm{3}^{\mathrm{2n}+\mathrm{3}} =\mathrm{m},\mathrm{find}\:\mathrm{3}^{−\mathrm{n}} \\ $$
Commented by chernoaguero@gmail.com last updated on 13/Sep/17
$$\mathrm{3}^{\mathrm{2}{n}} ×\mathrm{2}^{\mathrm{3}} ={m} \\ $$$$\mathrm{27}\left(\mathrm{3}^{{n}} \right)^{\mathrm{2}} ={m} \\ $$$$\frac{\mathrm{27}\left(\mathrm{3}^{{n}} \right)^{\mathrm{2}} }{\mathrm{27}}=\frac{{m}}{\mathrm{27}} \\ $$$$\left(\mathrm{3}^{{n}} \right)^{\mathrm{2}} =\frac{{m}}{\mathrm{27}} \\ $$$$\sqrt{\left(\mathrm{3}^{{n}} \right)^{\mathrm{2}} }=\sqrt{\frac{{m}}{\mathrm{27}}} \\ $$$$\mathrm{3}^{{n}} =\sqrt{\frac{{m}}{\mathrm{27}}} \\ $$$$\mathrm{3}^{−{n}} =\frac{\sqrt{\mathrm{27}}}{\:\sqrt{{m}}} \\ $$$$\:=\frac{\mathrm{3}\sqrt{\mathrm{3}{m}}}{{m}}\: \\ $$$${when}\:{m}>\mathrm{0} \\ $$