Solve 5^4/8-5^3/4+5^2/2

$$\frac { 5 ^ { 4 } } { 8 } - \frac { 5 ^ { 3 } } { 4 } + \frac { 5 ^ { 2 } } { 2 }$$

Evaluate

$$\frac{475}{8}=59.375$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$\frac{625}{8}-\frac{5^{3}}{4}+\frac{5^{2}}{2}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{625}{8}-\frac{125}{4}+\frac{5^{2}}{2}$$

Least common multiple of 8 and 4 is 8. Convert \frac{625}{8} and \frac{125}{4} to fractions with denominator 8.

$$\frac{625}{8}-\frac{250}{8}+\frac{5^{2}}{2}$$

Since \frac{625}{8} and \frac{250}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625-250}{8}+\frac{5^{2}}{2}$$

Subtract 250 from 625 to get 375.

$$\frac{375}{8}+\frac{5^{2}}{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{375}{8}+\frac{25}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{375}{8} and \frac{25}{2} to fractions with denominator 8.

$$\frac{375}{8}+\frac{100}{8}$$

Since \frac{375}{8} and \frac{100}{8} have the same denominator, add them by adding their numerators.

$$\frac{375+100}{8}$$

Add 375 and 100 to get 475.

$$\frac{475}{8}$$

Factor

$$\frac{5 ^ {2} \cdot 19}{2 ^ {3}} = 59\frac{3}{8} = 59.375$$