Question

Question was provided via image upload.

Explanation:

Step1: Recall exponent rule

Recall that \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). For the expression \(xy^{\frac{2}{9}}\), we can rewrite the exponent part.

Step2: Apply the rule to \(y^{\frac{2}{9}}\)

Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\), for \(y^{\frac{2}{9}}\), we have \(y^{\frac{2}{9}}=\sqrt[9]{y^2}\). Then the entire expression \(xy^{\frac{2}{9}}\) is \(x\sqrt[9]{y^2}\), which matches the fourth option (the one with \(x\) and \(\sqrt[9]{y^2}\) in a product, looking at the given options' formatting).

Answer:

The fourth option (the one with \(x\sqrt[9]{y^2}\) or the last circular option with \(x\) and \(\sqrt[9]{y^2}\) as per the image's layout)