Question Number 34081 by Aditya 879 last updated on 30/Apr/18
$$\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{4}\:.{find}\:{n}^{{n}.} \\ $$
Answered by math1967 last updated on 30/Apr/18
$$\mathrm{2}^{{n}} \left(\mathrm{1}−\mathrm{2}^{−\mathrm{1}} \right)=\mathrm{4} \\ $$$$\mathrm{2}^{{n}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{4} \\ $$$$\mathrm{2}^{{n}} ×\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{4} \\ $$$$\mathrm{2}^{{n}} =\mathrm{8}\therefore\mathrm{2}^{{n}} =\mathrm{2}^{\mathrm{3}} \:\therefore{n}=\mathrm{3}\:\therefore{n}^{{n}} =\mathrm{3}^{\mathrm{3}} =\mathrm{27} \\ $$