Solve (4)^77.6-(5.6+7/8)

$$( 4 ) ^ { 7 } 7.6 - ( 5.6 + \frac { 7 } { 8 } )$$

Evaluate

$$124511.925$$

Solution Steps

Calculate 4 to the power of 7 and get 16384.

$$16384\times 7.6-\left(5.6+\frac{7}{8}\right)$$

Multiply 16384 and 7.6 to get 124518.4.

$$124518.4-\left(5.6+\frac{7}{8}\right)$$

Convert decimal number 5.6 to fraction \frac{56}{10}. Reduce the fraction \frac{56}{10} to lowest terms by extracting and canceling out 2.

$$124518.4-\left(\frac{28}{5}+\frac{7}{8}\right)$$

Least common multiple of 5 and 8 is 40. Convert \frac{28}{5} and \frac{7}{8} to fractions with denominator 40.

$$124518.4-\left(\frac{224}{40}+\frac{35}{40}\right)$$

Since \frac{224}{40} and \frac{35}{40} have the same denominator, add them by adding their numerators.

$$124518.4-\frac{224+35}{40}$$

Add 224 and 35 to get 259.

$$124518.4-\frac{259}{40}$$

Convert decimal number 124518.4 to fraction \frac{1245184}{10}. Reduce the fraction \frac{1245184}{10} to lowest terms by extracting and canceling out 2.

$$\frac{622592}{5}-\frac{259}{40}$$

Least common multiple of 5 and 40 is 40. Convert \frac{622592}{5} and \frac{259}{40} to fractions with denominator 40.

$$\frac{4980736}{40}-\frac{259}{40}$$

Since \frac{4980736}{40} and \frac{259}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4980736-259}{40}$$

Subtract 259 from 4980736 to get 4980477.

$$\frac{4980477}{40}$$

Factor

$$\frac{3 \cdot 353 \cdot 4703}{5 \cdot 2 ^ {3}} = 124511\frac{37}{40} = 124511.925$$