Question

Simplify : $\frac{\{\sqrt[4]{4(625{)}^{-3}}\times \sqrt[5]{50.00001}\times \sqrt[3]{3729}\times \sqrt[3]{3(0.008{)}^{-2}}\}}{\{\sqrt[5]{5243}\times \sqrt[3]{3(125{)}^{-2}}\}}$

• A. $\frac{5}{12}$
• B. $\frac{3}{80}$
• C. $\frac{3}{2}$
• D. 5

Answer 1

Answer: (C)

$\frac{3}{2}$

$\frac{\{\sqrt[4]{4(625{)}^{-3}}\times \sqrt[5]{50.00001}\times \sqrt[3]{3729}\times \sqrt[3]{3(0.008{)}^{-2}}\}}{\{\sqrt[5]{5243}\times \sqrt[3]{3(125{)}^{-2}}\}}$
$\frac{\{5^{\frac{4\times -3}{4}}\times {0.1}^{\frac{5}{5}}\times 9^{\frac{3}{3}}\times {0.2}^{\frac{3\times -2}{3}}\}}{\{3^{\frac{5}{5}}\times 5^{\frac{3\times -2}{3}}\}}$
$\frac{\{5^{-3}\times {0.1}^1\times 9^1\times {0.2}^{-2}\}}{\{3^1\times 5^{-2}\}}$
$5^{-1}\times {0.1}^1\times 3^1\times {0.2}^{-2}$
$5^{-1}\times {0.1}^1\times 3^1\times {0.2}^{-2}=\frac{3}{2}$
Answer (C) $\frac{3}{2}$