Question

Evaluate :- $\frac{1}{3}{\left(\sqrt{2}\right)}^6\times {\left(25\right)}^{\frac{1}{2}}\times \frac{1}{5^3}$

Answer 1

Simplifying $\frac{1}{3}{\left(\sqrt{2}\right)}^6\times {\left(25\right)}^{1/2}\times \frac{1}{5^3}$

$\frac{1}{3}{\left(\sqrt{2}\right)}^6\times {\left(25\right)}^{1/2}\times \frac{1}{5^3}=\frac{1}{3}{\left({\left(\sqrt{2}\right)}^2\right)}^3\times {\left(\left(5^2\right)\right)}^{1/2}\times \frac{1}{5^3}$

$=\frac{1}{3}{\left(2\right)}^3\times 5\times \frac{1}{5^3}$

$=\frac{1}{3}\times 8\times \frac{1}{5^2}$

$=\frac{8}{75}$