Question

Simplify and express the result in its simplest form

$\sqrt{x^3{y}^3}÷\sqrt[3]{3x^4{y}^3}$

• A. $\sqrt[6]{6x{y}^3}$
• B. $\sqrt[2]{2x{y}^3}$
• C. $\sqrt[3]{3x{y}^3}$
• D. $\sqrt[4]{4x{y}^3}$

Answer 1

Answer: (A)

$\sqrt[6]{6x{y}^3}$

$\sqrt{x^3{y}^3}÷\sqrt[3]{3x^4{y}^3}$

$=x^{\frac{3}{2}}{y}^{\frac{3}{2}}÷x^{\frac{4}{3}}y$

$=x^{\frac{3}{2}-\frac{4}{3}}{y}^{\frac{3}{2}-1}$

$=x^{\frac{9-8}{6}}{y}^{\frac{1}{2}}$

$=\sqrt[6]{6x{y}^3}$