Question

how to evaluate this (i) ( 1024 )^{13 power}
(ii) (14641 28561 ) ^{14 power} with exact solution

Answer 1

$$\begin{gathered} \left(1\right). \\ {\left(1024\right)}^{1/3} \\ =\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2} \\ =8\times \sqrt[3]{2} \\ \left(2\right). \\ {\left(\frac{14641}{28561}\right)}^{1/4} \\ =\sqrt[4]{\frac{14641}{28561}} \\ =\sqrt[4]{\frac{11\times 11\times 11\times 11}{13\times 13\times 13\times 13}} \\ =\frac{11}{13} \end{gathered}$$