Solve ((5/2)^3:(2/5)^2)*(5/2)^-4=

$$( ( \frac { 5 } { 2 } ) ^ { 3 } : ( \frac { 2 } { 5 } ) ^ { 2 } ) \cdot ( \frac { 5 } { 2 } ) ^ { - 4 } =$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Calculate \frac{5}{2} to the power of 3 and get \frac{125}{8}.

$$\frac{\frac{125}{8}}{\left(\frac{2}{5}\right)^{2}}\times \left(\frac{5}{2}\right)^{-4}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{\frac{125}{8}}{\frac{4}{25}}\times \left(\frac{5}{2}\right)^{-4}$$

Divide \frac{125}{8} by \frac{4}{25} by multiplying \frac{125}{8} by the reciprocal of \frac{4}{25}.

$$\frac{125}{8}\times \frac{25}{4}\times \left(\frac{5}{2}\right)^{-4}$$

Multiply \frac{125}{8} and \frac{25}{4} to get \frac{3125}{32}.

$$\frac{3125}{32}\times \left(\frac{5}{2}\right)^{-4}$$

Calculate \frac{5}{2} to the power of -4 and get \frac{16}{625}.

$$\frac{3125}{32}\times \frac{16}{625}$$

Multiply \frac{3125}{32} and \frac{16}{625} to get \frac{5}{2}.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$