\[
a \frac{x}{y}=\sqrt[y]{a^{x}=(y \sqrt{a})^{x}}
\]
simplify

Step 1 ：The given equation seems to be a bit confusing due to the placement of the equal signs and brackets. It seems like there might be a mistake in the equation. However, if we assume that the equation is meant to be \(a \frac{x}{y}=\sqrt[y]{a^{x}}\) and \(\sqrt[y]{a^{x}}=(y \sqrt{a})^{x}\), we can solve these two equations separately.

Step 2 ：For the first equation \(a \frac{x}{y}=\sqrt[y]{a^{x}}\), we can simplify it by taking both sides to the power of y.

Step 3 ：For the second equation \(\sqrt[y]{a^{x}}=(y \sqrt{a})^{x}\), we can simplify it by taking both sides to the power of y/x.

Step 4 ：The equations did not simplify further. This is because the equations are already in their simplest form. Therefore, the simplified forms of the equations are \(a \frac{x}{y}=\sqrt[y]{a^{x}}\) and \(\sqrt[y]{a^{x}}=(y \sqrt{a})^{x}\).

Step 5 ：Final Answer: \(\boxed{a \frac{x}{y}=\sqrt[y]{a^{x}} \quad \text{and} \quad \sqrt[y]{a^{x}}=(y \sqrt{a})^{x}}\)