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

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

Evaluate

$$0.000262144$$

Solution Steps

Calculate 0.1 to the power of -3 and get 1000.

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

Calculate 5 to the power of -2 and get \frac{1}{25}.

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

Multiply 1000 and \frac{1}{25} to get 40.

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

Calculate 0.4 to the power of 3 and get 0.064.

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

Multiply \frac{5}{64} and 0.064 to get \frac{1}{200}.

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

Calculate \frac{1}{200} to the power of -2 and get 40000.

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

Reduce the fraction \frac{40}{40000} to lowest terms by extracting and canceling out 40.

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

Calculate \frac{1}{5} to the power of -2 and get 25.

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

Calculate 0.25 to the power of 2 and get 0.0625.

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

Multiply 25 and 0.0625 to get 1.5625.

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

Calculate 1.5625 to the power of -3 and get 0.262144.

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

Multiply \frac{1}{1000} and 0.262144 to get \frac{512}{1953125}.

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

Factor

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