Resolver frac{0.1^{-3}*5^{-2}}{(5/64*0.4^{3})^-2}*((1/5)^-2*0.25^2)^-3

$$\frac { 0.1 ^ { - 3 } \cdot 5 ^ { - 2 } } { ( \frac { 5 } { 64 } \cdot 0.4 ^ { 3 } ) ^ { - 2 } } \cdot ( ( \frac { 1 } { 5 } ) ^ { - 2 } \cdot 0.25 ^ { 2 } ) ^ { - 3 }$$

Calcular

$$0.000262144$$

Pasos da solución

Calcula 0.1 á potencia de -3 e obtén 1000.

$$\frac{1000\times 5^{-2}}{\left(\frac{5}{64}\times 0.4^{3}\right)^{-2}}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Calcula 5 á potencia de -2 e obtén \frac{1}{25}.

$$\frac{1000\times \frac{1}{25}}{\left(\frac{5}{64}\times 0.4^{3}\right)^{-2}}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Multiplica 1000 e \frac{1}{25} para obter 40.

$$\frac{40}{\left(\frac{5}{64}\times 0.4^{3}\right)^{-2}}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Calcula 0.4 á potencia de 3 e obtén 0.064.

$$\frac{40}{\left(\frac{5}{64}\times 0.064\right)^{-2}}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Multiplica \frac{5}{64} e 0.064 para obter \frac{1}{200}.

$$\frac{40}{\left(\frac{1}{200}\right)^{-2}}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Calcula \frac{1}{200} á potencia de -2 e obtén 40000.

$$\frac{40}{40000}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Reduce a fracción \frac{40}{40000} a termos máis baixos extraendo e cancelando 40.

$$\frac{1}{1000}\times \left(\left(\frac{1}{5}\right)^{-2}\times 0.25^{2}\right)^{-3}$$

Calcula \frac{1}{5} á potencia de -2 e obtén 25.

$$\frac{1}{1000}\times \left(25\times 0.25^{2}\right)^{-3}$$

Calcula 0.25 á potencia de 2 e obtén 0.0625.

$$\frac{1}{1000}\times \left(25\times 0.0625\right)^{-3}$$

Multiplica 25 e 0.0625 para obter 1.5625.

$$\frac{1}{1000}\times 1.5625^{-3}$$

Calcula 1.5625 á potencia de -3 e obtén 0.262144.

$$\frac{1}{1000}\times 0.262144$$

Multiplica \frac{1}{1000} e 0.262144 para obter \frac{512}{1953125}.

$$\frac{512}{1953125}$$

Factorizar

$$\frac{2 ^ {9}}{5 ^ {9}} = 0.000262144$$