Question

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

• A. $10$
• B. $1$
• C. $6$
• D. $18$

Answer 1

Answer: (A)

$10$

$\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times 4^{\frac{1}{4}}}{{10}^{-\frac{1}{5}}\times 5^{\frac{3}{5}}}÷\frac{4^{-\frac{2}{3}}\times 5^{-\frac{7}{5}}}{4^{\frac{3}{5}}\times 6^{-\frac{1}{3}}}$

$=\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times 4^{\frac{1}{4}}}{{10}^{-\frac{1}{5}}\times 5^{\frac{3}{5}}}\times \frac{4^{\frac{2}{3}}\times 5^{\frac{7}{5}}}{4^{-\frac{3}{5}}\times 6^{\frac{1}{3}}}$

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

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

$=2\times 5=10$