Question Number 68740 by ahmadshah last updated on 15/Sep/19
Commented by Prithwish sen last updated on 15/Sep/19
$$\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\mathrm{30}\left(\mathrm{30}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\left(\mathrm{30}\right)^{\mathrm{2}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\left(\mathrm{30}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} }}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}.\left(\mathrm{30}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\left(\mathrm{30}\right)^{\frac{\mathrm{9}}{\mathrm{4}}} }} \\ $$$$=\sqrt{\mathrm{30}.\left(\mathrm{30}\right)^{\frac{\mathrm{9}}{\mathrm{8}}} } \\ $$$$=\left(\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{8}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\:\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{16}}} \\ $$
Answered by MJS last updated on 15/Sep/19
$$\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{16}}} \\ $$