Question

Which expression is equivalent to? Please help! Screenshots attached.

Answer 1

Answer:

$\frac{\sqrt{5} }{x^{2} y}$

Step-by-step explanation:

That's a complex expression, let's simplify it, step by step, off the start, we'll simplify the 55/11:

$\sqrt{ \frac{55 x^{7} y^{6} }{11 x^{11} y^{8} } } = \sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } }$

Then we'll simplify the x's and y's:

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

Let's split the square root in two and solve the bottom part:

$\sqrt{ \frac{5}{x^{4} y^{2} } } = \frac{\sqrt{5} }{\sqrt{x^{4} y^{2}} } = \frac{\sqrt{5} }{x^{2} y}$

The solution is then:

$\frac{\sqrt{5} }{x^{2} y}$

Answer 2

Answer:

The expression which is equivalent to the given expression is:

          $\dfrac{\sqrt{5}}{x^2y}$

Step-by-step explanation:

We are given a expression as:

     $\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}$

Now we know that:

$55=11\times 5$

Hence, we get:

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

which is written as:

$\sqrt{\dfrac{5x^7y^6}{x^{11}y^8}}$

Also, we know that if n>m

Then

$\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}$

Hence, we have the expression as:

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

This could be given as:

$=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}$

Now, we know that:

$\sqrt{x^4}=\sqrt{(x^2)^2}=x^2\\\\and\\\\\sqrt{y^2}=y$

Hence, we get that:

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