Solve 2*390.6^2*42.9*3.412div14.4^2div300^2div2.412

$$2 \times { 390.6 }^{ 2 } \times 42.9 \times 3.412 \div { 14.4 }^{ 2 } \div { 300 }^{ 2 } \div 2.412$$

Evaluate

$$\frac{5743869131}{5788800000}\approx 0.99223831$$

Solution Steps

Express \frac{\frac{\frac{2\times 390.6^{2}\times 42.9\times 3.412}{14.4^{2}}}{300^{2}}}{2.412} as a single fraction.

$$\frac{\frac{2\times 390.6^{2}\times 42.9\times 3.412}{14.4^{2}}}{300^{2}\times 2.412}$$

Calculate 390.6 to the power of 2 and get 152568.36.

$$\frac{\frac{2\times 152568.36\times 42.9\times 3.412}{14.4^{2}}}{300^{2}\times 2.412}$$

Multiply 2 and 152568.36 to get 305136.72.

$$\frac{\frac{305136.72\times 42.9\times 3.412}{14.4^{2}}}{300^{2}\times 2.412}$$

Multiply 305136.72 and 42.9 to get 13090365.288.

$$\frac{\frac{13090365.288\times 3.412}{14.4^{2}}}{300^{2}\times 2.412}$$

Multiply 13090365.288 and 3.412 to get 44664326.362656.

$$\frac{\frac{44664326.362656}{14.4^{2}}}{300^{2}\times 2.412}$$

Calculate 14.4 to the power of 2 and get 207.36.

$$\frac{\frac{44664326.362656}{207.36}}{300^{2}\times 2.412}$$

Expand \frac{44664326.362656}{207.36} by multiplying both numerator and the denominator by 1000000.

$$\frac{\frac{44664326362656}{207360000}}{300^{2}\times 2.412}$$

Reduce the fraction \frac{44664326362656}{207360000} to lowest terms by extracting and canceling out 2592.

$$\frac{\frac{17231607393}{80000}}{300^{2}\times 2.412}$$

Calculate 300 to the power of 2 and get 90000.

$$\frac{\frac{17231607393}{80000}}{90000\times 2.412}$$

Multiply 90000 and 2.412 to get 217080.

$$\frac{\frac{17231607393}{80000}}{217080}$$

Express \frac{\frac{17231607393}{80000}}{217080} as a single fraction.

$$\frac{17231607393}{80000\times 217080}$$

Multiply 80000 and 217080 to get 17366400000.

$$\frac{17231607393}{17366400000}$$

Reduce the fraction \frac{17231607393}{17366400000} to lowest terms by extracting and canceling out 3.

$$\frac{5743869131}{5788800000}$$

Factor

$$\frac{11 \cdot 13 \cdot 853 \cdot 7 ^ {2} \cdot 31 ^ {2}}{67 \cdot 2 ^ {10} \cdot 3 ^ {3} \cdot 5 ^ {5}} = 0.9922383103579325$$