Solve (5/3)^2-(1/2)^3

$$( \frac { 5 } { 3 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{191}{72}\approx 2.652777778$$

Solution Steps

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{25}{9}-\left(\frac{1}{2}\right)^{3}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{25}{9}-\frac{1}{8}$$

Least common multiple of 9 and 8 is 72. Convert \frac{25}{9} and \frac{1}{8} to fractions with denominator 72.

$$\frac{200}{72}-\frac{9}{72}$$

Since \frac{200}{72} and \frac{9}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{200-9}{72}$$

Subtract 9 from 200 to get 191.

$$\frac{191}{72}$$

Factor

$$\frac{191}{2 ^ {3} \cdot 3 ^ {2}} = 2\frac{47}{72} = 2.6527777777777777$$