Respuesta :

WojtekR
[tex]\sqrt{\dfrac{128x^5y^6}{2x^7y^5}}=\sqrt{\dfrac{128}{2}\cdot\dfrac{x^5}{x^7}\cdot\dfrac{y^6}{y^5}}=\sqrt{64\cdot\dfrac{1}{x^2}\cdot y}=\sqrt{64}\cdot\sqrt{\dfrac{1}{x^2}}\cdot\sqrt{y}=\\\\\\=8\cdot\dfrac{1}{x}\cdot\sqrt{y}=\boxed{\dfrac{8\sqrt{y}}{x}}[/tex]

Answer D.

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is,

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

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

Use exponent rule [tex]\frac{a^m}{a^n}=a^{m-n}[/tex],

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

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

Use exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex],

[tex]\sqrt{64\times \frac{1}{x^2}\times y}[/tex]

[tex]\sqrt{(\frac{8}{x})^2\times y}[/tex]

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

Therefore option D is correct.

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