Question 36

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

Solution

we have :
$$\frac{\left(2^{\frac{1}{2}}\times\ 3^{\frac{1}{3}}\times\ 4^{\frac{1}{4}}\right)}{10^{-\frac{1}{5}}\times\ 5^{\frac{3}{5}}}\ \ \ \$$
Now 4 = 2^2 and 10 = 2*5
We get $$\ \frac{\left(2^{\frac{1}{2}+\frac{1}{2}}\times3^{\frac{1}{3}}\ \right)}{2^{-\frac{1}{5}}\times\ 5^{-\frac{1}{5}}\times\ 5^{\frac{3}{5}}}=\frac{\left(2^{\frac{6}{5}}\times\ 3^{\frac{1}{3}}\right)}{5^{\frac{2}{5}}}$$     (1)
Now the next term we have is :$$\frac{\left(3^{\frac{4}{3}}\times\ 5^{-\frac{7}{5}}\right)}{4^{-\frac{3}{5}}\times\ 6}$$
6= 2*3 and 4=2^2
We get $$\frac{\left(3^{\frac{1}{3}}\times\ 5^{-\frac{7}{5}}\right)}{2^{-\frac{1}{5}}}$$     (2)
Dividing (1) and (2) we get
$$\frac{\left(2^{\frac{6}{5}}\times\ 3^{\frac{1}{3}}\right)}{5^{\frac{2}{5}}}\times\ \frac{\left(2^{-\frac{1}{5}}\right)}{3^{\frac{1}{3}}\times\ 5^{-\frac{7}{5}}}$$
= $$\frac{2}{5^{-1}}=10$$
Now we have to multiply by 2
so we get 10*2=20

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