which expression is equivalent to $sqrt{\frac{55x^{7}y^{6}}{11x^{11}y^{8}}}$? assume $x > 0$ and $y >…

which expression is equivalent to $sqrt{\frac{55x^{7}y^{6}}{11x^{11}y^{8}}}$? assume $x > 0$ and $y > 0$.\n$\frac{x^{2}sqrt{5}}{y}$\n$\frac{ysqrt{5}}{x^{2}}$\n$\frac{sqrt{5}}{x^{2}y}$\n$\frac{xsqrt{5}}{y}$

which expression is equivalent to $sqrt{\frac{55x^{7}y^{6}}{11x^{11}y^{8}}}$? assume $x > 0$ and $y > 0$.\n$\frac{x^{2}sqrt{5}}{y}$\n$\frac{ysqrt{5}}{x^{2}}$\n$\frac{sqrt{5}}{x^{2}y}$\n$\frac{xsqrt{5}}{y}$

Answer

Explanation:

Step 1: Simplify the coefficient

Simplify $\frac{55}{11}$ to get $5$. $$ \frac{55}{11} = 5 $$

Step 2: Simplify the $x$ terms

Subtract exponents: $x^{7-11} = x^{-4} = \frac{1}{x^4}$. $$ x^{7} \div x^{11} = x^{-4} = \frac{1}{x^4} $$

Step 3: Simplify the $y$ terms

Subtract exponents: $y^{6-8} = y^{-2} = \frac{1}{y^2}$. $$ y^{6} \div y^{8} = y^{-2} = \frac{1}{y^2} $$

Step 4: Combine and apply the square root

Combine terms under the square root and simplify: $\sqrt{\frac{5}{x^4 y^2}} = \frac{\sqrt{5}}{x^2 y}$. $$ \sqrt{\frac{5}{x^4 y^2}} = \frac{\sqrt{5}}{\sqrt{x^4 y^2}} = \frac{\sqrt{5}}{x^2 y} $$

Answer:

$\frac{\sqrt{5}}{x^2 y}$ (corresponding to the third option)