Question

$\frac{\sqrt[6]{62}{[{\left(625\right)}^{\frac{3}{5}}\times {\left(1024\right)}^{-\frac{6}{5}}÷{\left(25\right)}^{\frac{3}{5}}]}^{\frac{1}{2}}}{\left[{\left(\sqrt[3]{3128}\right)}^{-\frac{5}{2}}\right]\times {\left(125\right)}^{\frac{1}{5}}}÷\frac{{\left({10}^3\right)}^2÷{\left({10}^2\right)}^3}{{\left({10}^2\right)}^3÷{\left({10}^3\right)}^2}$ equals

• A. $\frac{1}{5}$
• B. $\frac{1}{125}$
• C. 1
• D. $\frac{1}{10}$

Answer 1

Answer: (C)

1

$\frac{\sqrt[6]{62}{[{\left(625\right)}^{\frac{3}{5}}\times {\left(1024\right)}^{-\frac{6}{5}}÷{\left(25\right)}^{\frac{3}{5}}]}^{\frac{1}{2}}}{\left[{\left(\sqrt[3]{3128}\right)}^{-\frac{5}{2}}\right]\times {\left(125\right)}^{\frac{1}{5}}}÷\frac{{\left({10}^3\right)}^2÷{\left({10}^2\right)}^3}{{\left({10}^2\right)}^3÷{\left({10}^3\right)}^2}$
$\frac{\sqrt[6]{62}{[{\left(5^4\right)}^{\frac{3}{5}}\times {\left(2^{10}\right)}^{-\frac{6}{5}}÷{\left(5^2\right)}^{\frac{3}{5}}]}^{\frac{1}{2}}}{\left[{\left(\sqrt[3]{32^7}\right)}^{-\frac{5}{2}}\right]\times {\left(5^3\right)}^{\frac{1}{5}}}÷\frac{\frac{{10}^6}{{10}^6}}{\frac{{10}^6}{{10}^6}}$
$\frac{\sqrt[6]{62}[5^{4\cdot \frac{3}{5}\cdot \frac{1}{2}}\times 2^{10\cdot -\frac{6}{5}\cdot \frac{1}{2}}÷5^{2\cdot \frac{3}{5}\cdot \frac{1}{2}}]}{2^{7\cdot \frac{1}{3}\cdot -\frac{5}{2}}\times 5^{3\cdot \frac{1}{5}}}÷1$
$\frac{\sqrt[6]{62}[5^{\frac{6}{5}}\times 2^{-6}÷5^{\frac{3}{5}}]}{2^{-\frac{35}{6}}\times 5^{\frac{3}{5}}}÷1$
$\frac{\sqrt[6]{62}\left[5^{\frac{6}{5}-\frac{3}{5}}\right]}{2^{6-\frac{35}{6}}\times 5^{\frac{3}{5}}}÷1$
$\frac{\sqrt[6]{62}\left[5^{\frac{3}{5}}\right]}{2^{\frac{1}{6}}\times 5^{\frac{3}{5}}}÷1$
$\frac{\sqrt[6]{62}}{\sqrt[6]{62}}÷1$
$1÷1=1$