$$(\frac{5^{3}}{25^{2}})^{2}\times(\frac{8^{2}}{4^{2}})^{3}\times(\frac{5}{2})^{4}$$
$100$
$$\left(\frac{125}{25^{2}}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\left(\frac{125}{625}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\left(\frac{1}{5}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{1}{25}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{1}{25}\times \left(\frac{64}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{1}{25}\times \left(\frac{64}{16}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{1}{25}\times 4^{3}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{1}{25}\times 64\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{64}{25}\times \left(\frac{5}{2}\right)^{4}$$
$$\frac{64}{25}\times \frac{625}{16}$$
$$100$$
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$2^{2}\times 5^{2}$
