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

$$[ ( - \frac { 2 } { 5 } ) ^ { 2 } \cdot ( \frac { 1 } { 4 } ) ^ { 2 } ] ^ { 2 } : ( 5 ^ { 2 } \cdot 2 ^ { 2 } ) ^ { - 2 } - ( \frac { 4 } { 5 } ) ^ { - 5 } \cdot ( - \frac { 4 } { 5 } ) ^ { - 4 } : ( \frac { 4 } { 5 } ) ^ { - 7 }$$

Avaliar

$$-\frac{9}{16}=-0,5625$$

Passos Para a Resolução

Calcule -\frac{2}{5} elevado a 2 e obtenha \frac{4}{25}.

$$\frac{\left(\frac{4}{25}\times \left(\frac{1}{4}\right)^{2}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Calcule \frac{1}{4} elevado a 2 e obtenha \frac{1}{16}.

$$\frac{\left(\frac{4}{25}\times \frac{1}{16}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Multiplique \frac{4}{25} e \frac{1}{16} para obter \frac{1}{100}.

$$\frac{\left(\frac{1}{100}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Calcule \frac{1}{100} elevado a 2 e obtenha \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Calcule 5 elevado a 2 e obtenha 25.

$$\frac{\frac{1}{10000}}{\left(25\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Calcule 2 elevado a 2 e obtenha 4.

$$\frac{\frac{1}{10000}}{\left(25\times 4\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Multiplique 25 e 4 para obter 100.

$$\frac{\frac{1}{10000}}{100^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Calcule 100 elevado a -2 e obtenha \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\frac{1}{10000}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Dividir \frac{1}{10000} por \frac{1}{10000} para obter 1.

$$1-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Para dividir as potências da mesma base, subtraia o exponente do denominador do exponente do numerador.

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

Calcule -\frac{4}{5} elevado a -4 e obtenha \frac{625}{256}.

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

Calcule \frac{4}{5} elevado a 2 e obtenha \frac{16}{25}.

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

Multiplique \frac{625}{256} e \frac{16}{25} para obter \frac{25}{16}.

$$1-\frac{25}{16}$$

Subtraia \frac{25}{16} de 1 para obter -\frac{9}{16}.

$$-\frac{9}{16}$$

Fatorizar

$$-\frac{9}{16} = -0,5625$$