Solve (-4/5)^3*5^2*(-1/2)^5*(1/2)^-3

$$( - \frac { 4 } { 5 } ) ^ { 3 } \times 5 ^ { 2 } \times ( - \frac { 1 } { 2 } ) ^ { 5 } \times ( \frac { 1 } { 2 } ) ^ { - 3 }$$

Evaluate

$$\frac{16}{5}=3.2$$

Solution Steps

Calculate -\frac{4}{5} to the power of 3 and get -\frac{64}{125}.

$$-\frac{64}{125}\times 5^{2}\left(-\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{-3}$$

Calculate 5 to the power of 2 and get 25.

$$-\frac{64}{125}\times 25\left(-\frac{1}{2}\right)^{5}\times \left(\frac{1}{2}\right)^{-3}$$

Multiply -\frac{64}{125} and 25 to get -\frac{64}{5}.

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

Calculate -\frac{1}{2} to the power of 5 and get -\frac{1}{32}.

$$-\frac{64}{5}\left(-\frac{1}{32}\right)\times \left(\frac{1}{2}\right)^{-3}$$

Multiply -\frac{64}{5} and -\frac{1}{32} to get \frac{2}{5}.

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

Calculate \frac{1}{2} to the power of -3 and get 8.

$$\frac{2}{5}\times 8$$

Multiply \frac{2}{5} and 8 to get \frac{16}{5}.

$$\frac{16}{5}$$

Factor

$$\frac{2 ^ {4}}{5} = 3\frac{1}{5} = 3.2$$