Question

Simplified form of
${[\sqrt[3]{3x^{4}y}\times \frac{1}{\sqrt[4]{4x^2{y}^8}}]}^{-6}$

• A. $x^5.y^{10}$
• B. $\frac{y^{10}}{x^5}$
• C. $\frac{y^2}{x}$
• D. $\frac{y^5}{x^5}$

Answer 1

Answer: (B)

$\frac{y^{10}}{x^5}$

${\left[\right(x^4.y{)}^{\frac{1}{3}}.\frac{1}{(x^2.y^8{)}^{\frac{1}{4}}}]}^{-6}$
$={[x^{\frac{4}{3}}.y^{\frac{1}{3}}\times \frac{1}{(x^{\frac{2}{4}}.y^{\frac{8}{4}})}]}^{-6}$
$={[x^{\frac{4}{3}-\frac{1}{2}}\times y^{\frac{1}{3}-2}]}^{-6}={[x^{\frac{8-3}{6}}.y^{\frac{1-6}{3}}]}^{-6}$
$=(x^{\frac{5}{6}}.y^{-\frac{5}{3}}{)}^{-6}=x^{\frac{5}{6}\times -6}.y^{-\frac{5}{3}\times -6}$
$=x^{-5}\times y^{+10}=\frac{y^{10}}{x^5}$