Solve (28/3)^3-14(28/3)^2

$$( \frac { 28 } { 3 } ) ^ { 3 } - 14 ( \frac { 28 } { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{10976}{27}\approx -406.518518519$$

Solution Steps

Calculate \frac{28}{3} to the power of 3 and get \frac{21952}{27}.

$$\frac{21952}{27}-14\times \left(\frac{28}{3}\right)^{2}$$

Calculate \frac{28}{3} to the power of 2 and get \frac{784}{9}.

$$\frac{21952}{27}-14\times \frac{784}{9}$$

Express 14\times \frac{784}{9} as a single fraction.

$$\frac{21952}{27}-\frac{14\times 784}{9}$$

Multiply 14 and 784 to get 10976.

$$\frac{21952}{27}-\frac{10976}{9}$$

Least common multiple of 27 and 9 is 27. Convert \frac{21952}{27} and \frac{10976}{9} to fractions with denominator 27.

$$\frac{21952}{27}-\frac{32928}{27}$$

Since \frac{21952}{27} and \frac{32928}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21952-32928}{27}$$

Subtract 32928 from 21952 to get -10976.

$$-\frac{10976}{27}$$

Factor

$$-\frac{10976}{27} = -406\frac{14}{27} = -406.51851851851853$$