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

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

Calcula

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

Passos de solució

Calculeu -\frac{2}{5} elevat a 2 per obtenir \frac{4}{25}.

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

Calculeu \frac{1}{4} elevat a 2 per obtenir \frac{1}{16}.

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

Multipliqueu \frac{4}{25} per \frac{1}{16} per obtenir \frac{1}{100}.

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

Calculeu \frac{1}{100} elevat a 2 per obtenir \frac{1}{10000}.

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

Calculeu 5 elevat a 2 per obtenir 25.

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

Calculeu 2 elevat a 2 per obtenir 4.

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

Multipliqueu 25 per 4 per obtenir 100.

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

Calculeu 100 elevat a -2 per obtenir \frac{1}{10000}.

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

Dividiu \frac{1}{10000} entre \frac{1}{10000} per obtenir 1.

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

Per dividir potències de la mateixa base, resteu l'exponent del denominador de l'exponent del numerador.

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

Calculeu -\frac{4}{5} elevat a -4 per obtenir \frac{625}{256}.

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

Calculeu \frac{4}{5} elevat a 2 per obtenir \frac{16}{25}.

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

Multipliqueu \frac{625}{256} per \frac{16}{25} per obtenir \frac{25}{16}.

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

Resteu 1 de \frac{25}{16} per obtenir -\frac{9}{16}.

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

Factoritzar

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