Resolver [(-2/5)^{2}*(1/4)^{2}]^{2}:(5^{2}*2^{2})^-2-(4/5)^-5*(-4/5)^-4:(frac{4}{5})^-7

Calcular

Pasos da solución

Factorizar

Quiz

Arithmetic

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Copiado a portapapeis

\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}}

Calcula -\frac{2}{5} á potencia de 2 e obtén \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}}

Calcula \frac{1}{4} á potencia de 2 e obtén \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}}

Multiplica \frac{4}{25} e \frac{1}{16} para obter \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}}

Calcula \frac{1}{100} á potencia de 2 e obtén \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}}

Calcula 5 á potencia de 2 e obtén 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}}

Calcula 2 á potencia de 2 e obtén 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}}

Multiplica 25 e 4 para obter 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}}

Calcula 100 á potencia de -2 e obtén \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} entre \frac{1}{10000} para obter 1.

1-\left(-\frac{4}{5}\right)^{-4}\times \left(\frac{4}{5}\right)^{2}

Para dividir potencias da mesma base, resta o expoñente do denominador do expoñente do numerador.

1-\frac{625}{256}\times \left(\frac{4}{5}\right)^{2}

Calcula -\frac{4}{5} á potencia de -4 e obtén \frac{625}{256}.

1-\frac{625}{256}\times \frac{16}{25}