Question

Which expression is equivalent to...

Answer 1

Answer:

C

Step-by-step explanation:

Use exponents property:

$\dfrac{x^a}{x^b}=x^{a-b}$

1. Note that

$\dfrac{x^7}{x^{11}}=x^{7-11}=x^{-4}=\dfrac{1}{x^4}$

and

$\dfrac{y^6}{y^8}=y^{6-8}=y^{-2}=\dfrac{1}{y^2}$

2. Now

$\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{5}{x^4y^2}}=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}=\dfrac{\sqrt{5}}{x^2y}$

because $x>0,\ y>0$