Respuesta :

sylvain96

Answer:

[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]

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:

[tex]\sqrt{ \frac{55 x^{7} y^{6} }{11 x^{11} y^{8} } } = \sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } }[/tex]

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

[tex]\sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } } = \sqrt{ \frac{5}{x^{4} y^{2} } }[/tex]

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

[tex]\sqrt{ \frac{5}{x^{4} y^{2} } } = \frac{\sqrt{5} }{\sqrt{x^{4} y^{2}} } = \frac{\sqrt{5} }{x^{2} y}[/tex]

The solution is then:

[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]

Answer:

The expression which is equivalent to the given expression is:

          [tex]\dfrac{\sqrt{5}}{x^2y}[/tex]

Step-by-step explanation:

We are given a expression as:

     [tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}[/tex]

Now we know that:

[tex]55=11\times 5[/tex]

Hence, we get:

 [tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{11\times 5x^7y^6}{11x^{11}y^8}[/tex]

which is written as:

[tex]\sqrt{\dfrac{5x^7y^6}{x^{11}y^8}}[/tex]

Also, we know that if n>m

Then

[tex]\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}[/tex]

Hence, we have the expression as:

[tex]=\sqrt{\dfrac{5}{x^{11-7}y^{8-6}}}\\\\\\=\sqrt{\dfrac{5}{x^4y^2}[/tex]

This could be given as:

[tex]=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}[/tex]

Now, we know that:

[tex]\sqrt{x^4}=\sqrt{(x^2)^2}=x^2\\\\and\\\\\sqrt{y^2}=y[/tex]

Hence, we get that:

[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\dfrac{\sqrt{5}}{x^2y}[/tex]

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