Answer: Last option.
Step-by-step explanation:
Given the expression:
[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}[/tex]
The Quotient of powers property states that:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
And the Power of a powet property states that:
[tex](a^m)^n=a^{mn}[/tex]
Then, applying these properties, you get:
[tex]=\sqrt{\frac{(2^3)^26y}{x^2}[/tex]
Now you must remember that:
[tex]\sqrt[a]{a^n}=a[/tex]
Therefore, simpliying the expression, you get:
[tex]=\frac{2^3\sqrt{y}}{x}=\frac{8\sqrt{y}}{x}[/tex]
