Respuesta :

absor201

Answer:

Last option

Step-by-step explanation:

Given expression is:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5} }[/tex]

The terms can be simplified one by one

[tex]=\sqrt{\frac{64x^5y^6}{x^7y^5} }[/tex]

As the larger power of x is in numerator, the smaller power will be brought to denominator

[tex]=\sqrt{\frac{64y^6}{x^{(7-5)}y^5}}\\=\sqrt{\frac{64y^6}{x^{2}y^5}}[/tex]

Similarly for y,

[tex]=\sqrt{\frac{64y^{(6-5)}}{x^{2}}}\\=\sqrt{\frac{64y}{x^{2}}}[/tex]

Applying the radical

[tex]\sqrt{\frac{8^2*y}{x^{2}}}\\So\ the\ answer\ will\ be\\= \frac{8\sqrt{y}}{x}[/tex]

So, last option is the correct answer ..

luisejr77

Answer: Last option.

Step-by-step explanation:

You need to apply the Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

Then:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}} =\sqrt{\frac{64y}{x^2}}[/tex]

Remember that:

[tex]64=8*8=8^2[/tex]

Then you can rewrite the expression:

[tex]=\sqrt{\frac{8^2y}{x^2}}[/tex]

Finally, since [tex]\sqrt[n]{a^n}=a[/tex], you get:

[tex]=\frac{8\sqrt{y} }{x}[/tex]