$$(\frac{x^{2}}{y^{2}})^{2}$$
$\left(\frac{x}{y}\right)^{4}$
$$\left(\frac{x^{2}}{y^{2}}\right)^{2}$$
$$\frac{\left(x^{2}\right)^{2}}{\left(y^{2}\right)^{2}}$$
$$\frac{x^{2\times 2}}{y^{2\times 2}}$$
$$\frac{x^{4}}{y^{2\times 2}}$$
$$\frac{x^{4}}{y^{4}}$$
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