Which expression is equivalent to? Assume x 0 and y > 0.algebra II engenuity

Answer:Last optionStep-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 ..