Solve frac{25^frac{5{2}}*7291/3}{125^frac{2{3}}*27^frac{2{3}}*8^frac{4{3}}}

$$\frac { 25 ^ { \frac { 5 } { 2 } } \times 729 \frac { 1 } { 3 } } { 125 ^ { \frac { 2 } { 3 } } \times 27 ^ { \frac { 2 } { 3 } } \times 8 ^ { \frac { 4 } { 3 } } }$$

Evaluate

$$\frac{68375}{108}\approx 633.101851852$$

Solution Steps

Calculate 25 to the power of \frac{5}{2} and get 3125.

$$\frac{3125\times \frac{729\times 3+1}{3}}{125^{\frac{2}{3}}\times 27^{\frac{2}{3}}\times 8^{\frac{4}{3}}}$$

Multiply 729 and 3 to get 2187.

$$\frac{3125\times \frac{2187+1}{3}}{125^{\frac{2}{3}}\times 27^{\frac{2}{3}}\times 8^{\frac{4}{3}}}$$

Add 2187 and 1 to get 2188.

$$\frac{3125\times \frac{2188}{3}}{125^{\frac{2}{3}}\times 27^{\frac{2}{3}}\times 8^{\frac{4}{3}}}$$

Multiply 3125 and \frac{2188}{3} to get \frac{6837500}{3}.

$$\frac{\frac{6837500}{3}}{125^{\frac{2}{3}}\times 27^{\frac{2}{3}}\times 8^{\frac{4}{3}}}$$

Calculate 125 to the power of \frac{2}{3} and get 25.

$$\frac{\frac{6837500}{3}}{25\times 27^{\frac{2}{3}}\times 8^{\frac{4}{3}}}$$

Calculate 27 to the power of \frac{2}{3} and get 9.

$$\frac{\frac{6837500}{3}}{25\times 9\times 8^{\frac{4}{3}}}$$

Multiply 25 and 9 to get 225.

$$\frac{\frac{6837500}{3}}{225\times 8^{\frac{4}{3}}}$$

Calculate 8 to the power of \frac{4}{3} and get 16.

$$\frac{\frac{6837500}{3}}{225\times 16}$$

Multiply 225 and 16 to get 3600.

$$\frac{\frac{6837500}{3}}{3600}$$

Express \frac{\frac{6837500}{3}}{3600} as a single fraction.

$$\frac{6837500}{3\times 3600}$$

Multiply 3 and 3600 to get 10800.

$$\frac{6837500}{10800}$$

Reduce the fraction \frac{6837500}{10800} to lowest terms by extracting and canceling out 100.

$$\frac{68375}{108}$$

Factor

$$\frac{5 ^ {3} \cdot 547}{2 ^ {2} \cdot 3 ^ {3}} = 633\frac{11}{108} = 633.1018518518518$$