Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{(-25)}^{2}}\times {10}^{-2}{(\frac{1}{2})}^{-2}\]
Since the power of 2 is even, the result will be positive.
\[\frac{1}{{25}^{2}}\times {10}^{-2}{(\frac{1}{2})}^{-2}\]
Simplify \({25}^{2}\) to \(625\).
\[\frac{1}{625}\times {10}^{-2}{(\frac{1}{2})}^{-2}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{625}\times {10}^{-2}\times \frac{1}{{(\frac{1}{2})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{1}{625}\times {10}^{-2}\times \frac{1}{\frac{1}{{2}^{2}}}\]
Simplify \({2}^{2}\) to \(4\).
\[\frac{1}{625}\times {10}^{-2}\times \frac{1}{\frac{1}{4}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1\times {10}^{-2}\times 1}{625\times \frac{1}{4}}\]
Simplify \(1\times {10}^{-2}\) to \({10}^{-2}\).
\[\frac{{10}^{-2}\times 1}{625\times \frac{1}{4}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{10}^{2}}\times 1}{625\times \frac{1}{4}}\]
Simplify \({10}^{2}\) to \(100\).
\[\frac{\frac{1}{100}\times 1}{625\times \frac{1}{4}}\]
Simplify \(\frac{1}{100}\times 1\) to \(\frac{1}{100}\).
\[\frac{\frac{1}{100}}{625\times \frac{1}{4}}\]
Simplify \(625\times \frac{1}{4}\) to \(\frac{625}{4}\).
\[\frac{\frac{1}{100}}{\frac{625}{4}}\]
Invert and multiply.
\[\frac{1}{100}\times \frac{4}{625}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1\times 4}{100\times 625}\]
Simplify \(1\times 4\) to \(4\).
\[\frac{4}{100\times 625}\]
Simplify \(100\times 625\) to \(62500\).
\[\frac{4}{62500}\]
Simplify.
\[\frac{1}{15625}\]
1/15625
