Solve (-62/93)^3div(-85/51)^2*(65/52)^3=

$$( - \frac { 62 } { 93 } ) ^ { 3 } \div ( - \frac { 85 } { 51 } ) ^ { 2 } \times ( \frac { 65 } { 52 } ) ^ { 3 } =$$

Evaluate

$$-\frac{5}{24}\approx -0.208333333$$

Solution Steps

Reduce the fraction \frac{62}{93} to lowest terms by extracting and canceling out 31.

$$\frac{\left(-\frac{2}{3}\right)^{3}}{\left(-\frac{85}{51}\right)^{2}}\times \left(\frac{65}{52}\right)^{3}$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{-\frac{8}{27}}{\left(-\frac{85}{51}\right)^{2}}\times \left(\frac{65}{52}\right)^{3}$$

Reduce the fraction \frac{85}{51} to lowest terms by extracting and canceling out 17.

$$\frac{-\frac{8}{27}}{\left(-\frac{5}{3}\right)^{2}}\times \left(\frac{65}{52}\right)^{3}$$

Calculate -\frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{-\frac{8}{27}}{\frac{25}{9}}\times \left(\frac{65}{52}\right)^{3}$$

Divide -\frac{8}{27} by \frac{25}{9} by multiplying -\frac{8}{27} by the reciprocal of \frac{25}{9}.

$$-\frac{8}{27}\times \frac{9}{25}\times \left(\frac{65}{52}\right)^{3}$$

Multiply -\frac{8}{27} and \frac{9}{25} to get -\frac{8}{75}.

$$-\frac{8}{75}\times \left(\frac{65}{52}\right)^{3}$$

Reduce the fraction \frac{65}{52} to lowest terms by extracting and canceling out 13.

$$-\frac{8}{75}\times \left(\frac{5}{4}\right)^{3}$$

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

$$-\frac{8}{75}\times \frac{125}{64}$$

Multiply -\frac{8}{75} and \frac{125}{64} to get -\frac{5}{24}.

$$-\frac{5}{24}$$

Factor

$$-\frac{5}{24} = -0.20833333333333334$$