Solve (75/35*20/8)^6*2/3+3/4

$$( \frac { 75 } { 35 } \times \frac { 20 } { 8 } ) ^ { 6 } \times \frac { 2 } { 3 } + \frac { 3 } { 4 }$$

Evaluate

$$\frac{59328995451}{3764768}\approx 15759.004393099$$

Solution Steps

Reduce the fraction \frac{75}{35} to lowest terms by extracting and canceling out 5.

$$\left(\frac{15}{7}\times \frac{20}{8}\right)^{6}\times \frac{2}{3}+\frac{3}{4}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\left(\frac{15}{7}\times \frac{5}{2}\right)^{6}\times \frac{2}{3}+\frac{3}{4}$$

Multiply \frac{15}{7} and \frac{5}{2} to get \frac{75}{14}.

$$\left(\frac{75}{14}\right)^{6}\times \frac{2}{3}+\frac{3}{4}$$

Calculate \frac{75}{14} to the power of 6 and get \frac{177978515625}{7529536}.

$$\frac{177978515625}{7529536}\times \frac{2}{3}+\frac{3}{4}$$

Multiply \frac{177978515625}{7529536} and \frac{2}{3} to get \frac{59326171875}{3764768}.

$$\frac{59326171875}{3764768}+\frac{3}{4}$$

Add \frac{59326171875}{3764768} and \frac{3}{4} to get \frac{59328995451}{3764768}.

$$\frac{59328995451}{3764768}$$

Factor

$$\frac{3 \cdot 11 \cdot 107 \cdot 16802321}{2 ^ {5} \cdot 7 ^ {6}} = 15759\frac{16539}{3764768} = 15759.004393099389$$