Question

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

• A. 5
• B. 6
• C. 10
• D. 15
• E. 30

Answer 1

The correct option is C

10

The given expression

$\begin{array}{c}\frac{2^{1/2}.3^{1/3}.{{\left(2\right)}^2}^{1/4}}{{\left(2\times 5\right)}^{-1/5}.5^{3/5}}\times \frac{{\left(2^2\right)}^{-3/5}\times 2\times 3}{3^{4/3}\times 5^{-7/5}}\\ =\frac{2^{\left(\frac{1}{2}+\frac{1}{2}\right)}.3^{1/3}}{2^{-1/5}\times 5^{\left(\frac{3}{5}-\frac{1}{5}\right)}}\times \frac{2^{-6/5}\times 2\times 3}{3^{4/3}\times 5^{-7/5}}\\ =2^{\left(1+1/5-6/5+1\right)}\times 3^{\left(\frac{1}{3}+1-\frac{4}{3}\right)}\times 5^{\left(\frac{7}{5}-\frac{2}{5}\right)}\\ =2^1\times 3^0\times 5^1=10.\end{array}$