Solve 1/1*1+2/11^2+2/11^3+2/1.1^4+frac{2}{11^3}+frac{0*5}{1{1}^6}-4

$$\frac{ 1 }{ 1 \cdot 1 } + \frac{ 2 }{ 1 { 1 }^{ 2 } } + \frac{ 2 }{ 1 { 1 }^{ 3 } } + \frac{ 2 }{ { 1.1 }^{ 4 } } + \frac{ 2 }{ 1 { 1 }^{ 3 } } + \frac{ 0 \cdot 5 }{ 1 { 1 }^{ 6 } } -4$$

Evaluate

$$\frac{63923}{14641}\approx 4.366026911$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{1}{1\times 1}+\frac{2}{1^{3}}+\frac{2}{1\times 1^{3}}+\frac{2}{1.1^{4}}+\frac{2}{1\times 1^{3}}+\frac{0\times 5}{1\times 1^{6}}-4$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{1\times 1}+\frac{2}{1^{3}}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1\times 1^{3}}+\frac{0\times 5}{1\times 1^{6}}-4$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{1\times 1}+\frac{2}{1^{3}}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1\times 1^{6}}-4$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{1}{1\times 1}+\frac{2}{1^{3}}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Multiply 1 and 1 to get 1.

$$\frac{1}{1}+\frac{2}{1^{3}}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Anything divided by one gives itself.

$$1+\frac{2}{1^{3}}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Calculate 1 to the power of 3 and get 1.

$$1+\frac{2}{1}+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Anything divided by one gives itself.

$$1+2+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Add 1 and 2 to get 3.

$$3+\frac{2}{1^{4}}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Calculate 1 to the power of 4 and get 1.

$$3+\frac{2}{1}+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Anything divided by one gives itself.

$$3+2+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Add 3 and 2 to get 5.

$$5+\frac{2}{1.1^{4}}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Calculate 1.1 to the power of 4 and get 1.4641.

$$5+\frac{2}{1.4641}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Expand \frac{2}{1.4641} by multiplying both numerator and the denominator by 10000.

$$5+\frac{20000}{14641}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Convert 5 to fraction \frac{73205}{14641}.

$$\frac{73205}{14641}+\frac{20000}{14641}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Since \frac{73205}{14641} and \frac{20000}{14641} have the same denominator, add them by adding their numerators.

$$\frac{73205+20000}{14641}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Add 73205 and 20000 to get 93205.

$$\frac{93205}{14641}+\frac{2}{1^{4}}+\frac{0\times 5}{1^{7}}-4$$

Calculate 1 to the power of 4 and get 1.

$$\frac{93205}{14641}+\frac{2}{1}+\frac{0\times 5}{1^{7}}-4$$

Anything divided by one gives itself.

$$\frac{93205}{14641}+2+\frac{0\times 5}{1^{7}}-4$$

Convert 2 to fraction \frac{29282}{14641}.

$$\frac{93205}{14641}+\frac{29282}{14641}+\frac{0\times 5}{1^{7}}-4$$

Since \frac{93205}{14641} and \frac{29282}{14641} have the same denominator, add them by adding their numerators.

$$\frac{93205+29282}{14641}+\frac{0\times 5}{1^{7}}-4$$

Add 93205 and 29282 to get 122487.

$$\frac{122487}{14641}+\frac{0\times 5}{1^{7}}-4$$

Multiply 0 and 5 to get 0.

$$\frac{122487}{14641}+\frac{0}{1^{7}}-4$$

Calculate 1 to the power of 7 and get 1.

$$\frac{122487}{14641}+\frac{0}{1}-4$$

Anything divided by one gives itself.

$$\frac{122487}{14641}+0-4$$

Add \frac{122487}{14641} and 0 to get \frac{122487}{14641}.

$$\frac{122487}{14641}-4$$

Convert 4 to fraction \frac{58564}{14641}.

$$\frac{122487}{14641}-\frac{58564}{14641}$$

Since \frac{122487}{14641} and \frac{58564}{14641} have the same denominator, subtract them by subtracting their numerators.

$$\frac{122487-58564}{14641}$$

Subtract 58564 from 122487 to get 63923.

$$\frac{63923}{14641}$$

Factor

$$\frac{97 \cdot 659}{11 ^ {4}} = 4\frac{5359}{14641} = 4.366026910730142$$