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\frac{\left(\frac{4}{25}\times \left(\frac{1}{4}\right)^{2}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate -\frac{2}{5} to the power of 2 and get \frac{4}{25}.
\frac{\left(\frac{4}{25}\times \frac{1}{16}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.
\frac{\left(\frac{1}{100}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Multiply \frac{4}{25} and \frac{1}{16} to get \frac{1}{100}.
\frac{\frac{1}{10000}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate \frac{1}{100} to the power of 2 and get \frac{1}{10000}.
\frac{\frac{1}{10000}}{\left(25\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate 5 to the power of 2 and get 25.
\frac{\frac{1}{10000}}{\left(25\times 4\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate 2 to the power of 2 and get 4.
\frac{\frac{1}{10000}}{100^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Multiply 25 and 4 to get 100.
\frac{\frac{1}{10000}}{\frac{1}{10000}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Calculate 100 to the power of -2 and get \frac{1}{10000}.
1-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}
Divide \frac{1}{10000} by \frac{1}{10000} to get 1.
1-\left(-\frac{4}{5}\right)^{-4}\times \left(\frac{4}{5}\right)^{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
1-\frac{625}{256}\times \left(\frac{4}{5}\right)^{2}
Calculate -\frac{4}{5} to the power of -4 and get \frac{625}{256}.
1-\frac{625}{256}\times \frac{16}{25}
Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.
1-\frac{25}{16}
Multiply \frac{625}{256} and \frac{16}{25} to get \frac{25}{16}.
-\frac{9}{16}
Subtract \frac{25}{16} from 1 to get -\frac{9}{16}.