Question

simplify (root 2/5)^8 divided by(root 2/10)^13

Answer 1

Dear student
$$\begin{gathered} {\left(\frac{\sqrt{2}}{5}\right)}^8÷{\left(\frac{\sqrt{2}}{10}\right)}^{13} \\ ={\left(\frac{\sqrt{2}}{5}\right)}^8\times {\left(\frac{10}{\sqrt{2}}\right)}^{13} \\ ={\left(\sqrt{2}\right)}^8\times \frac{1}{5^8}\times {\left(2\times 5\right)}^{13}\times \frac{1}{{\left(\sqrt{2}\right)}^{13}} \\ =\frac{1}{{\left(\sqrt{2}\right)}^5}\times 5^5\times 2^{13} \\ =\frac{1}{2^2\sqrt{2}}\times 5^5\times 2^{13} \\ =\frac{1}{\sqrt{2}}\times 5^5\times 2^{11} \\ =5^5\times 2^{10}\sqrt{2} \end{gathered}$$
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