Solve frac{{125}^frac{2{3}}}{2433/5}div3^4

$$\frac{ { 125 }^{ \frac{ 2 }{ 3 } } }{ 243 \frac{ 3 }{ 5 } } \div { 3 }^{ 4 }$$

Evaluate

$$\frac{125}{98658}\approx 0.001267003$$

Solution Steps

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

$$\frac{\frac{25}{\frac{243\times 5+3}{5}}}{3^{4}}$$

Multiply 243 and 5 to get 1215.

$$\frac{\frac{25}{\frac{1215+3}{5}}}{3^{4}}$$

Add 1215 and 3 to get 1218.

$$\frac{\frac{25}{\frac{1218}{5}}}{3^{4}}$$

Divide 25 by \frac{1218}{5} by multiplying 25 by the reciprocal of \frac{1218}{5}.

$$\frac{25\times \frac{5}{1218}}{3^{4}}$$

Multiply 25 and \frac{5}{1218} to get \frac{125}{1218}.

$$\frac{\frac{125}{1218}}{3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{125}{1218}}{81}$$

Express \frac{\frac{125}{1218}}{81} as a single fraction.

$$\frac{125}{1218\times 81}$$

Multiply 1218 and 81 to get 98658.

$$\frac{125}{98658}$$

Factor

$$\frac{5 ^ {3}}{2 \cdot 3 ^ {5} \cdot 7 \cdot 29} = 0.001267003182711995$$