Question

The value of $\frac{2^{\frac{1}{2}}{.3}^{\frac{1}{3}}{.4}^{\frac{1}{4}}}{{10}^{-\frac{1}{5}}{.5}^{\frac{3}{5}}}÷\frac{3^{\frac{4}{3}}{.5}^{-\frac{7}{5}}}{4^{-\frac{3}{5}}.6}$ is:

• A. $5$
• B. $6$
• C. $10$
• D. $15$

Answer 1

The correct option is C $10$

Given exp $=\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times (2^2{)}^{\frac{1}{4}}}{(2\times 5{)}^{-\frac{1}{5}}\times 5^{\frac{3}{5}}}÷\frac{3^{\frac{4}{3}}\times 5^{-\frac{7}{5}}}{(2^2{)}^{\frac{-3}{5}}\times 2\times 3}$

$=\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times (2{)}^{\frac{1}{2}}}{(2{)}^{-\frac{1}{5}}\times 5^{-\frac{1}{5}}\times 5^{\frac{3}{5}}}\times \frac{(2{)}^{\frac{-6}{5}}\times 2\times 3}{3^{\frac{4}{3}}\times 5^{-\frac{7}{5}}}$

$=\frac{2^{(\frac{1}{2}+\frac{1}{2}-\frac{6}{5}+1+\frac{1}{5})}\times 3^{(\frac{1}{3}+1-\frac{4}{3})}}{5^{(-\frac{1}{5}+\frac{3}{5}-\frac{7}{5})}}$

$=\frac{2\times 3^0}{5^{-1}}=2\times 5=10$