Equivalent expressions SAT question

Choice B is correct. For positive values of $a$ and $b$, $a^m{b}^m={(ab)}^m$, $\sqrt[n]{a}={(a)}^{\frac{1}{n}}$, and ${(a^j)}^k=a^{jk}$. Therefore, the given expression, $\sqrt[7]{x^9{y}^9}$, can be rewritten as $\sqrt[7]{{(xy)}^9}$. This expression is equivalent to ${({(xy)}^9)}^{\frac{1}{7}}$, which can be rewritten as ${(xy)}^{9\cdot \frac{1}{7}}$, or ${(xy)}^{\frac{9}{7}}$. 

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.