Solve (62/93)^3+(-85/51)^2*(65/52)^8=

$$( \frac { 62 } { 93 } ) ^ { 3 } + ( - \frac { 85 } { 51 } ) ^ { 2 } \times ( \frac { 65 } { 52 } ) ^ { 8 } =$$

Evaluate

$$\frac{29821163}{1769472}\approx 16.853142067$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{8}{27}+\frac{25}{9}\times \left(\frac{5}{4}\right)^{8}$$

Calculate \frac{5}{4} to the power of 8 and get \frac{390625}{65536}.

$$\frac{8}{27}+\frac{25}{9}\times \frac{390625}{65536}$$

Multiply \frac{25}{9} and \frac{390625}{65536} to get \frac{9765625}{589824}.

$$\frac{8}{27}+\frac{9765625}{589824}$$

Add \frac{8}{27} and \frac{9765625}{589824} to get \frac{29821163}{1769472}.

$$\frac{29821163}{1769472}$$

Factor

$$\frac{31 \cdot 961973}{2 ^ {16} \cdot 3 ^ {3}} = 16\frac{1509611}{1769472} = 16.853142067238135$$