Which expression is equivalent to $\sqrt[4]{\frac{16 x^{11} y^8}{81 x^7 y^6}}$ ? Assume $x>0$ and $y=0$.
A. $\frac{4 x\left(\sqrt[4]{y^2}\right)}{9}$
B. $\frac{2 x\left(\sqrt{y^2}\right)}{3}$
C. $\frac{4 x^2 y}{9}$
D. $\frac{2 x^2 y}{3}
Answer (2)
The equivalent expression is 3 2 x y , which corresponds to option B. It is derived by simplifying the original expression step-by-step and extracting roots from the components. This approach enables clear understanding of how the expression reduces down to its final form.
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⁴√16x¹¹y⁸ / 81x⁷y⁶ = 3 2 x y ;
