Question

Simplify

$\sqrt{x^6{y}^3}÷\sqrt[3]{3x^{2}y}$

• A. $\sqrt[6]{6x^{14}{y}^7}$
• B. $\sqrt[6]{6x^{14}{y}^3}$
• C. $\sqrt[6]{6x^7{y}^7}$
• D. $\sqrt[6]{6x^4{y}^7}$

Answer 1

The correct option is A $\sqrt[6]{6x^{14}{y}^7}$

$\sqrt{x^6{y}^3}÷\sqrt[3]{3x^{2}y}$
$=\frac{\sqrt{x^6{y}^3}}{\sqrt[3]{3x^{2}y}}$
$=\frac{{\left(x^6{y}^3\right)}^{\frac{1}{2}}}{{\left(x^{2}y\right)}^{\frac{1}{3}}}$
$=\frac{{\left(x^{2}y\right)}^{\frac{3}{2}}}{{\left(x^{2}y\right)}^{\frac{1}{3}}}$
$=\frac{{\left(x^{2}y\right)}^{\frac{9}{6}}}{{\left(x^{2}y\right)}^{\frac{2}{6}}}$
$={\left[\frac{{\left(x^{2}y\right)}^9}{{\left(x^{2}y\right)}^2}\right]}^{\frac{1}{6}}$
$={\left\{{\left(x^{2}y\right)}^7\right\}}^{\frac{1}{6}}$
$=\sqrt[6]{6x^{14}{y}^7}$