Dear Student, 1215271552 = 12271552 = 122715×52 = 122712 = 1227 = 2×2×33×3×3 = 2333 = 23Using properties of exponents: (xa)b = xab Regards

please simplify it

Dear Student,

{(\frac{12^{\frac{1}{5}}}{27^{\frac{1}{5}}})}^{\frac{5}{2}} = {[{(\frac{12}{27})}^{\frac{1}{5}}]}^{\frac{5}{2}} = {(\frac{12}{27})}^{\frac{1}{5} \times \frac{5}{2}} = {(\frac{12}{27})}^{\frac{1}{2}} = \frac{\sqrt{12}}{\sqrt{27}} = \frac{\sqrt{2 \times 2 \times 3}}{\sqrt{3 \times 3 \times 3}} = \frac{2 \sqrt{3}}{3 \sqrt{3}} = \frac{2}{3} U s i n g p r o p e r t i e s o f e x p o n e n t s : {(x^{a})}^{b} = x^{a b}

Regards