Solve (2^9/9+2^6/3+2^3/3)-(1/9+frac{1}{3}+frac{1}{3})

$$( \frac { 2 ^ { 9 } } { 9 } + \frac { 2 ^ { 6 } } { 3 } + \frac { 2 ^ { 3 } } { 3 } ) - ( \frac { 1 } { 9 } + \frac { 1 } { 3 } + \frac { 1 } { 3 } )$$

Evaluate

$$\frac{721}{9}\approx 80.111111111$$

Solution Steps

Calculate 2 to the power of 9 and get 512.

$$\frac{512}{9}+\frac{2^{6}}{3}+\frac{2^{3}}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Calculate 2 to the power of 6 and get 64.

$$\frac{512}{9}+\frac{64}{3}+\frac{2^{3}}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{512}{9} and \frac{64}{3} to fractions with denominator 9.

$$\frac{512}{9}+\frac{192}{9}+\frac{2^{3}}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Since \frac{512}{9} and \frac{192}{9} have the same denominator, add them by adding their numerators.

$$\frac{512+192}{9}+\frac{2^{3}}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Add 512 and 192 to get 704.

$$\frac{704}{9}+\frac{2^{3}}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{704}{9}+\frac{8}{3}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{704}{9} and \frac{8}{3} to fractions with denominator 9.

$$\frac{704}{9}+\frac{24}{9}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Since \frac{704}{9} and \frac{24}{9} have the same denominator, add them by adding their numerators.

$$\frac{704+24}{9}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Add 704 and 24 to get 728.

$$\frac{728}{9}-\left(\frac{1}{9}+\frac{1}{3}+\frac{1}{3}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{1}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{728}{9}-\left(\frac{1}{9}+\frac{3}{9}+\frac{1}{3}\right)$$

Since \frac{1}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{728}{9}-\left(\frac{1+3}{9}+\frac{1}{3}\right)$$

Add 1 and 3 to get 4.

$$\frac{728}{9}-\left(\frac{4}{9}+\frac{1}{3}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{728}{9}-\left(\frac{4}{9}+\frac{3}{9}\right)$$

Since \frac{4}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{728}{9}-\frac{4+3}{9}$$

Add 4 and 3 to get 7.

$$\frac{728}{9}-\frac{7}{9}$$

Since \frac{728}{9} and \frac{7}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{728-7}{9}$$

Subtract 7 from 728 to get 721.

$$\frac{721}{9}$$

Factor

$$\frac{7 \cdot 103}{3 ^ {2}} = 80\frac{1}{9} = 80.11111111111111$$