Question

$\frac{2 {}^{1 \div 3} }{8 {}^{1 \div 2} } \times \frac{12 {}^{1 \div 2} }{10 {}^{1 \div 3} } \times \frac{27 {}^{1 \div 2} }{18 {}^{1 \div 2} } \times \frac{5 {}^{1 \div 2} }{81 {}^{1 \div 4} }$
please solve it answer aana chahiye 1/2
solve it for 100 points​

Answer 1

Answer:

The answer to this question is $\frac{1}{2}\cdot 5^{\frac{1}{6}}$

Step-by-step explanation:

If $\frac{1}{2}$ is the answer to your question then please check the question

$\frac{2^\frac{1}{3}}{8^\frac{1}{2}}\times \frac{12^\frac{1}{2}}{10^\frac{1}{3}}\times \frac{27^\frac{1}{2}}{18^\frac{1}{2}}\times \frac{5^\frac{1}{2}}{81^\frac{1}{4}}\\\\= \frac{2^\frac{1}{3}}{2^\frac{3}{2}}\times \frac{4^\frac{1}{2}\cdot 3^\frac{1}{2}}{2^\frac{1}{3}\cdot 5^\frac{1}{3}}\times \frac{3^\frac{3}{2}}{2^\frac{1}{2}\cdot 9^\frac{1}{2}}\times \frac{5^\frac{1}{2}}{3}$

$= \frac{2^\frac{1}{3}}{2^\frac{3}{2}}\times \frac{2\cdot 3^\frac{1}{2}}{2^\frac{1}{3}\cdot 5^\frac{1}{3}}\times \frac{3^\frac{3}{2}}{2^\frac{1}{2}\cdot 3}\times \frac{5^\frac{1}{2}}{3}$

$=2^{\frac{1}{3}-\frac{3}{2} - \frac{1}{3} +1-\frac{1}{2}}\cdot 3^{\frac{1}{2}+\frac{3}{2} - 1-1}\cdot 5^{\frac{1}{2} - \frac{1}{3}}\\= 2^{-1}\cdot 3^0\cdot 5^\frac{1}{6}\\= \frac{1}{2}\cdot 5^{\frac{1}{6}}$