which expression is equivalent to $xy^{\frac{2}{9}}$?\n$sqrt{xy^{9}}$\n$sqrt9{xy^{2}}$\n$x(sqrt{y^{9}})$\n$x(…

which expression is equivalent to $xy^{\frac{2}{9}}$?\n$sqrt{xy^{9}}$\n$sqrt9{xy^{2}}$\n$x(sqrt{y^{9}})$\n$x(sqrt9{y^{2}})$

which expression is equivalent to $xy^{\frac{2}{9}}$?\n$sqrt{xy^{9}}$\n$sqrt9{xy^{2}}$\n$x(sqrt{y^{9}})$\n$x(sqrt9{y^{2}})$

Answer

Explanation:

Step1: Recall exponent - radical conversion rule

The rule for converting a fractional - exponent to a radical is $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. For the term $y^{\frac{2}{9}}$, where $a = y$, $m = 2$, and $n = 9$, we have $y^{\frac{2}{9}}=\sqrt[9]{y^{2}}$.

Step2: Consider the entire expression

The original expression is $xy^{\frac{2}{9}}$. Substituting the radical form of $y^{\frac{2}{9}}$, we get $x\sqrt[9]{y^{2}}$.

Answer:

D. $x\left(\sqrt[9]{y^{2}}\right)$