Solve (1/273^3+2*3)-(1/271^3+2*1)

$$( \frac{ 1 }{ 27 } { 3 }^{ 3 } +2 \cdot 3)-( \frac{ 1 }{ 27 } { 1 }^{ 3 } +2 \cdot 1)$$

Evaluate

$$\frac{134}{27}\approx 4.962962963$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{1}{27}\times 27+2\times 3-\left(\frac{1}{27}\times 1^{3}+2\times 1\right)$$

Cancel out 27 and 27.

$$1+2\times 3-\left(\frac{1}{27}\times 1^{3}+2\times 1\right)$$

Multiply 2 and 3 to get 6.

$$1+6-\left(\frac{1}{27}\times 1^{3}+2\times 1\right)$$

Add 1 and 6 to get 7.

$$7-\left(\frac{1}{27}\times 1^{3}+2\times 1\right)$$

Calculate 1 to the power of 3 and get 1.

$$7-\left(\frac{1}{27}\times 1+2\times 1\right)$$

Multiply \frac{1}{27} and 1 to get \frac{1}{27}.

$$7-\left(\frac{1}{27}+2\times 1\right)$$

Multiply 2 and 1 to get 2.

$$7-\left(\frac{1}{27}+2\right)$$

Convert 2 to fraction \frac{54}{27}.

$$7-\left(\frac{1}{27}+\frac{54}{27}\right)$$

Since \frac{1}{27} and \frac{54}{27} have the same denominator, add them by adding their numerators.

$$7-\frac{1+54}{27}$$

Add 1 and 54 to get 55.

$$7-\frac{55}{27}$$

Convert 7 to fraction \frac{189}{27}.

$$\frac{189}{27}-\frac{55}{27}$$

Since \frac{189}{27} and \frac{55}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{189-55}{27}$$

Subtract 55 from 189 to get 134.

$$\frac{134}{27}$$

Factor

$$\frac{2 \cdot 67}{3 ^ {3}} = 4\frac{26}{27} = 4.962962962962963$$