Solve 714.2^2+64.3/82/14.2^2-410.2214.2^4

$$\frac{ \frac{ 7 { 14.2 }^{ 2 } +64.3 }{ 82 } }{ { 14.2 }^{ 2 } } -410.22 { 14.2 }^{ 4 }$$

Evaluate

$$-\frac{215452122574344617}{12917562500}\approx -16679007.558457303$$

Solution Steps

Calculate 14.2 to the power of 2 and get 201.64.

$$\frac{\frac{7\times 201.64+64.3}{82}}{14.2^{2}}-410.22\times 14.2^{4}$$

Multiply 7 and 201.64 to get 1411.48.

$$\frac{\frac{1411.48+64.3}{82}}{14.2^{2}}-410.22\times 14.2^{4}$$

Add 1411.48 and 64.3 to get 1475.78.

$$\frac{\frac{1475.78}{82}}{14.2^{2}}-410.22\times 14.2^{4}$$

Expand \frac{1475.78}{82} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{147578}{8200}}{14.2^{2}}-410.22\times 14.2^{4}$$

Reduce the fraction \frac{147578}{8200} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{73789}{4100}}{14.2^{2}}-410.22\times 14.2^{4}$$

Calculate 14.2 to the power of 2 and get 201.64.

$$\frac{\frac{73789}{4100}}{201.64}-410.22\times 14.2^{4}$$

Express \frac{\frac{73789}{4100}}{201.64} as a single fraction.

$$\frac{73789}{4100\times 201.64}-410.22\times 14.2^{4}$$

Multiply 4100 and 201.64 to get 826724.

$$\frac{73789}{826724}-410.22\times 14.2^{4}$$

Calculate 14.2 to the power of 4 and get 40658.6896.

$$\frac{73789}{826724}-410.22\times 40658.6896$$

Multiply 410.22 and 40658.6896 to get 16679007.647712.

$$\frac{73789}{826724}-16679007.647712$$

Convert decimal number 16679007.647712 to fraction \frac{16679007647712}{1000000}. Reduce the fraction \frac{16679007647712}{1000000} to lowest terms by extracting and canceling out 32.

$$\frac{73789}{826724}-\frac{521218988991}{31250}$$

Least common multiple of 826724 and 31250 is 12917562500. Convert \frac{73789}{826724} and \frac{521218988991}{31250} to fractions with denominator 12917562500.

$$\frac{1152953125}{12917562500}-\frac{215452123727297742}{12917562500}$$

Since \frac{1152953125}{12917562500} and \frac{215452123727297742}{12917562500} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1152953125-215452123727297742}{12917562500}$$

Subtract 215452123727297742 from 1152953125 to get -215452122574344617.

$$-\frac{215452122574344617}{12917562500}$$

Factor

$$-\frac{215452122574344617}{12917562500} = -16679007\frac{7213907108}{12917562500} = -16679007.558457302$$