Which expression is equivalent to sqrt [7](x^9y^9) where a and y are positive? A (xy)^(7)/(9) B (xy)^(9)/(7) C (xy)^16 D (xy)^63 (D

To find the expression equivalent to $\sqrt [7]{x^{9}y^{9}}$, we need to simplify the radical expression.<br /><br />The given expression is $\sqrt [7]{x^{9}y^{9}}$, which can be written as $(x^{9}y^{9})^{\frac{1}{7}}$.<br /><br />Using the property of exponents, we can simplify this expression further.<br /><br />$(x^{9}y^{9})^{\frac{1}{7}} = x^{9 \cdot \frac{1}{7}}y^{9 \cdot \frac{1}{7}} = x^{\frac{9}{7}}y^{\frac{9}{7}}$.<br /><br />Therefore, the expression equivalent to $\sqrt [7]{x^{9}y^{9}}$ is $(xy)^{\frac{9}{7}}$.<br /><br />So, the correct answer is option B: $(xy)^{\frac{9}{7}}$.