Solve (2^10/10-2^8/4+2^6/6)*3

$$( \frac { 2 ^ { 10 } } { 10 } - \frac { 2 ^ { 8 } } { 4 } + \frac { 2 ^ { 6 } } { 6 } ) \times 3$$

Evaluate

$$\frac{736}{5}=147.2$$

Solution Steps

Calculate 2 to the power of 10 and get 1024.

$$\left(\frac{1024}{10}-\frac{2^{8}}{4}+\frac{2^{6}}{6}\right)\times 3$$

Reduce the fraction \frac{1024}{10} to lowest terms by extracting and canceling out 2.

$$\left(\frac{512}{5}-\frac{2^{8}}{4}+\frac{2^{6}}{6}\right)\times 3$$

Calculate 2 to the power of 8 and get 256.

$$\left(\frac{512}{5}-\frac{256}{4}+\frac{2^{6}}{6}\right)\times 3$$

Divide 256 by 4 to get 64.

$$\left(\frac{512}{5}-64+\frac{2^{6}}{6}\right)\times 3$$

Convert 64 to fraction \frac{320}{5}.

$$\left(\frac{512}{5}-\frac{320}{5}+\frac{2^{6}}{6}\right)\times 3$$

Since \frac{512}{5} and \frac{320}{5} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{512-320}{5}+\frac{2^{6}}{6}\right)\times 3$$

Subtract 320 from 512 to get 192.

$$\left(\frac{192}{5}+\frac{2^{6}}{6}\right)\times 3$$

Calculate 2 to the power of 6 and get 64.

$$\left(\frac{192}{5}+\frac{64}{6}\right)\times 3$$

Reduce the fraction \frac{64}{6} to lowest terms by extracting and canceling out 2.

$$\left(\frac{192}{5}+\frac{32}{3}\right)\times 3$$

Least common multiple of 5 and 3 is 15. Convert \frac{192}{5} and \frac{32}{3} to fractions with denominator 15.

$$\left(\frac{576}{15}+\frac{160}{15}\right)\times 3$$

Since \frac{576}{15} and \frac{160}{15} have the same denominator, add them by adding their numerators.

$$\frac{576+160}{15}\times 3$$

Add 576 and 160 to get 736.

$$\frac{736}{15}\times 3$$

Express \frac{736}{15}\times 3 as a single fraction.

$$\frac{736\times 3}{15}$$

Multiply 736 and 3 to get 2208.

$$\frac{2208}{15}$$

Reduce the fraction \frac{2208}{15} to lowest terms by extracting and canceling out 3.

$$\frac{736}{5}$$

Factor

$$\frac{2 ^ {5} \cdot 23}{5} = 147\frac{1}{5} = 147.2$$