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

$$[ ( - 1 ) ^ { 4 } : ( \frac { 2 } { 5 } ) ^ { 3 } ] \cdot ( \frac { 5 } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{3125}{128}=24.4140625$$

Solution Steps

Calculate -1 to the power of 4 and get 1.

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

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

$$\frac{1}{\frac{8}{125}}\times \left(\frac{5}{4}\right)^{2}$$

Divide 1 by \frac{8}{125} by multiplying 1 by the reciprocal of \frac{8}{125}.

$$1\times \frac{125}{8}\times \left(\frac{5}{4}\right)^{2}$$

Multiply 1 and \frac{125}{8} to get \frac{125}{8}.

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

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{125}{8}\times \frac{25}{16}$$

Multiply \frac{125}{8} times \frac{25}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\times 25}{8\times 16}$$

Do the multiplications in the fraction \frac{125\times 25}{8\times 16}.

$$\frac{3125}{128}$$

Factor

$$\frac{5 ^ {5}}{2 ^ {7}} = 24\frac{53}{128} = 24.4140625$$