Since the power of 4 is even, the result will be positive.
\[\frac{{(\frac{1}{2})}^{4}\times \frac{625}{16}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{{2}^{4}}\times \frac{625}{16}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Simplify \({2}^{4}\) to \(16\).
\[\frac{\frac{1}{16}\times \frac{625}{16}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\frac{1\times 625}{16\times 16}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Simplify \(1\times 625\) to \(625\).
\[\frac{\frac{625}{16\times 16}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Simplify \(16\times 16\) to \(256\).
\[\frac{\frac{625}{256}}{{(\frac{5}{2})}^{4}\times \frac{1}{16}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{625}{256}}{\frac{{5}^{4}}{{2}^{4}}\times \frac{1}{16}}\]
Simplify \({5}^{4}\) to \(625\).
\[\frac{\frac{625}{256}}{\frac{625}{{2}^{4}}\times \frac{1}{16}}\]
Simplify \({2}^{4}\) to \(16\).
\[\frac{\frac{625}{256}}{\frac{625}{16}\times \frac{1}{16}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\frac{625}{256}}{\frac{625\times 1}{16\times 16}}\]
Simplify \(625\times 1\) to \(625\).
\[\frac{\frac{625}{256}}{\frac{625}{16\times 16}}\]
Simplify \(16\times 16\) to \(256\).
\[\frac{\frac{625}{256}}{\frac{625}{256}}\]
Cancel denominators.
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