The value of frac{2^{1 / 2} cdot 3^{1 / 3} cd | vedclass

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Question

(C) Given expression: $\frac{2^{1 / 2} \cdot 3^{1 / 3} \cdot 4^{1 / 4}}{10^{-1 / 5} \cdot 5^{3 / 5}} \div \frac{3^{4 / 3} \cdot 5^{-7 / 5}}{4^{-3 / 5}

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Given expression: $\frac{2^{1 / 2} \cdot 3^{1 / 3} \cdot 4^{1 / 4}}{10^{-1 / 5} \cdot 5^{3 / 5}} \div \frac{3^{4 / 3} \cdot 5^{-7 / 5}}{4^{-3 / 5} \cdot 6}$$= \left( \frac{2^{1 / 2} \cdot 3^{1 / 3} \cdot (2^2)^{1 / 4}}{10^{-1 / 5} \cdot 5^{3 / 5}} \right) \cdot \left( \frac{4^{-3 / 5} \cdot 6}{3^{4 / 3} \cdot 5^{-7 / 5}} \right)$$= \left( \frac{2^{1 / 2} \cdot 3^{1 / 3} \cdot 2^{1 / 2} \cdot 10^{1 / 5}}{5^{3 / 5}} \right) \cdot \left( \frac{(2^2)^{-3 / 5} \cdot (2 \cdot 3)}{3^{4 / 3} \cdot 5^{-7 / 5}} \right)$$= \left( \frac{2^{1} \cdot 3^{1 / 3} \cdot 2^{1 / 5} \cdot 5^{1 / 5}}{5^{3 / 5}} \right) \cdot \left( \frac{2^{-6 / 5} \cdot 2^1 \cdot 3^1}{3^{4 / 3} \cdot 5^{-7 / 5}} \right)$$= 2^{(1 + 1/5 - 6/5 + 1)} \cdot 3^{(1/3 + 1 - 4/3)} \cdot 5^{(1/5 - 3/5 + 7/5)}$$= 2^{(1 + 1/5 - 6/5 + 1)} \cdot 3^{(4/3 - 4/3)} \cdot 5^{(5/5)}$$= 2^1 \cdot 3^0 \cdot 5^1 = 2 \cdot 1 \cdot 5 = 10$

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

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