Question

Write the expression in the simplest form $\frac{\sqrt[6]{6x^{10}{y}^{12}}}{\sqrt[3]{3x^5{y}^6}}$.

• A. $1$
• B. $2$
• C. $x^2{y}^3\sqrt{x}$
• D. $x{y}^2\sqrt[3]{3x^2}$

Answer 1

Answer: (A)

$1$

$\frac{\sqrt[6]{6x^{10}{y}^{12}}}{\sqrt[3]{3x^5{y}^6}}=\frac{x^{\frac{10}{6}}{y}^{\frac{12}{6}}}{x^{\frac{5}{3}}{y}^{\frac{6}{3}}}$

$=x^{\frac{10}{6}-\frac{5}{3}}{y}^{\frac{12}{6}-\frac{6}{3}}=x^{\frac{10}{6}-\frac{10}{6}}\times y^{\frac{12}{6}-\frac{12}{6}}=x^0{y}^0=1\cdot 1=1$