Solve ((-3/5)^3+7/25)div(5/2)^3

$$( ( - \frac { 3 } { 5 } ) ^ { 3 } + \frac { 7 } { 25 } ) \div ( \frac { 5 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{64}{15625}=0.004096$$

Solution Steps

Calculate -\frac{3}{5} to the power of 3 and get -\frac{27}{125}.

$$\frac{-\frac{27}{125}+\frac{7}{25}}{\left(\frac{5}{2}\right)^{3}}$$

Least common multiple of 125 and 25 is 125. Convert -\frac{27}{125} and \frac{7}{25} to fractions with denominator 125.

$$\frac{-\frac{27}{125}+\frac{35}{125}}{\left(\frac{5}{2}\right)^{3}}$$

Since -\frac{27}{125} and \frac{35}{125} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-27+35}{125}}{\left(\frac{5}{2}\right)^{3}}$$

Add -27 and 35 to get 8.

$$\frac{\frac{8}{125}}{\left(\frac{5}{2}\right)^{3}}$$

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

$$\frac{\frac{8}{125}}{\frac{125}{8}}$$

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

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

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

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

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

$$\frac{64}{15625}$$

Factor

$$\frac{2 ^ {6}}{5 ^ {6}} = 0.004096$$