Solve 1/22.718^4+2.718^3/2.718^2-2*2.718+1-2.7718^2

$$\frac{ \frac{ 1 }{ 2 } { 2.718 }^{ 4 } + { 2.718 }^{ 3 } }{ { 2.718 }^{ 2 } -2 \cdot 2.718+1 } - { 2.7718 }^{ 2 }$$

Evaluate

$$\frac{154317843733889}{18447025000000}\approx 8.365459674$$

Solution Steps

Calculate 2.718 to the power of 4 and get 54.575510850576.

$$\frac{\frac{1}{2}\times 54.575510850576+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Convert decimal number 54.575510850576 to fraction \frac{13643877712644}{10000000000}. Reduce the fraction \frac{13643877712644}{10000000000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1}{2}\times \frac{3410969428161}{62500000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Multiply \frac{1}{2} times \frac{3410969428161}{62500000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 3410969428161}{2\times 62500000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Do the multiplications in the fraction \frac{1\times 3410969428161}{2\times 62500000000}.

$$\frac{\frac{3410969428161}{125000000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Calculate 2.718 to the power of 3 and get 20.079290232.

$$\frac{\frac{3410969428161}{125000000000}+20.079290232}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Convert decimal number 20.079290232 to fraction \frac{20079290232}{1000000000}. Reduce the fraction \frac{20079290232}{1000000000} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{3410969428161}{125000000000}+\frac{2509911279}{125000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Least common multiple of 125000000000 and 125000000 is 125000000000. Convert \frac{3410969428161}{125000000000} and \frac{2509911279}{125000000} to fractions with denominator 125000000000.

$$\frac{\frac{3410969428161}{125000000000}+\frac{2509911279000}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Since \frac{3410969428161}{125000000000} and \frac{2509911279000}{125000000000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3410969428161+2509911279000}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Add 3410969428161 and 2509911279000 to get 5920880707161.

$$\frac{\frac{5920880707161}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Calculate 2.718 to the power of 2 and get 7.387524.

$$\frac{\frac{5920880707161}{125000000000}}{7.387524-2\times 2.718+1}-2.7718^{2}$$

Multiply 2 and 2.718 to get 5.436.

$$\frac{\frac{5920880707161}{125000000000}}{7.387524-5.436+1}-2.7718^{2}$$

Subtract 5.436 from 7.387524 to get 1.951524.

$$\frac{\frac{5920880707161}{125000000000}}{1.951524+1}-2.7718^{2}$$

Add 1.951524 and 1 to get 2.951524.

$$\frac{\frac{5920880707161}{125000000000}}{2.951524}-2.7718^{2}$$

Express \frac{\frac{5920880707161}{125000000000}}{2.951524} as a single fraction.

$$\frac{5920880707161}{125000000000\times 2.951524}-2.7718^{2}$$

Multiply 125000000000 and 2.951524 to get 368940500000.

$$\frac{5920880707161}{368940500000}-2.7718^{2}$$

Calculate 2.7718 to the power of 2 and get 7.68287524.

$$\frac{5920880707161}{368940500000}-7.68287524$$

Convert decimal number 7.68287524 to fraction \frac{768287524}{100000000}. Reduce the fraction \frac{768287524}{100000000} to lowest terms by extracting and canceling out 4.

$$\frac{5920880707161}{368940500000}-\frac{192071881}{25000000}$$

Least common multiple of 368940500000 and 25000000 is 18447025000000. Convert \frac{5920880707161}{368940500000} and \frac{192071881}{25000000} to fractions with denominator 18447025000000.

$$\frac{296044035358050}{18447025000000}-\frac{141726191624161}{18447025000000}$$

Since \frac{296044035358050}{18447025000000} and \frac{141726191624161}{18447025000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{296044035358050-141726191624161}{18447025000000}$$

Subtract 141726191624161 from 296044035358050 to get 154317843733889.

$$\frac{154317843733889}{18447025000000}$$

Factor

$$\frac{11 \cdot 29 \cdot 61 \cdot 7930409771}{2 ^ {6} \cdot 5 ^ {8} \cdot 859 ^ {2}} = 8\frac{6741643733889}{18447025000000} = 8.365459673518576$$