1. **State the problem:** Find the equivalent expression with rational exponents for $\left(\sqrt{2xy}\right)^3$. 2. **Rewrite the square root as a rational exponent:** The square root means to the power of $\frac{1}{2}$, so $$\sqrt{2xy} = (2xy)^{\frac{1}{2}}$$ 3. **Apply the cube power:** $$\left((2xy)^{\frac{1}{2}}\right)^3 = (2xy)^{\frac{1}{2} \times 3} = (2xy)^{\frac{3}{2}}$$ 4. **Match the result with given options:** Option B is $(2xy)^{\frac{3}{2}}$. **Answer:** B. $(2xy)^{\frac{3}{2}}$