Solve 1/63/2+5^7-3^7/6

$$\frac{ 1 }{ 6 } \frac{ 3 }{ 2 } + \frac{ { 5 }^{ 7 } - { 3 }^{ 7 } }{ 6 }$$

Evaluate

$$\frac{151879}{12}\approx 12656.583333333$$

Solution Steps

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{6\times 2}+\frac{5^{7}-3^{7}}{6}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$\frac{3}{12}+\frac{5^{7}-3^{7}}{6}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}+\frac{5^{7}-3^{7}}{6}$$

Calculate 5 to the power of 7 and get 78125.

$$\frac{1}{4}+\frac{78125-3^{7}}{6}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{1}{4}+\frac{78125-2187}{6}$$

Subtract 2187 from 78125 to get 75938.

$$\frac{1}{4}+\frac{75938}{6}$$

Reduce the fraction \frac{75938}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\frac{37969}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{37969}{3} to fractions with denominator 12.

$$\frac{3}{12}+\frac{151876}{12}$$

Since \frac{3}{12} and \frac{151876}{12} have the same denominator, add them by adding their numerators.

$$\frac{3+151876}{12}$$

Add 3 and 151876 to get 151879.

$$\frac{151879}{12}$$

Factor

$$\frac{7 \cdot 13 \cdot 1669}{2 ^ {2} \cdot 3} = 12656\frac{7}{12} = 12656.583333333334$$