Solve (4/3)^3-2(4/3)^2

$$( \frac { 4 } { 3 } ) ^ { 3 } - 2 ( \frac { 4 } { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{32}{27}\approx -1.185185185$$

Solution Steps

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{64}{27}-2\times \left(\frac{4}{3}\right)^{2}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{64}{27}-2\times \frac{16}{9}$$

Express 2\times \frac{16}{9} as a single fraction.

$$\frac{64}{27}-\frac{2\times 16}{9}$$

Multiply 2 and 16 to get 32.

$$\frac{64}{27}-\frac{32}{9}$$

Least common multiple of 27 and 9 is 27. Convert \frac{64}{27} and \frac{32}{9} to fractions with denominator 27.

$$\frac{64}{27}-\frac{96}{27}$$

Since \frac{64}{27} and \frac{96}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-96}{27}$$

Subtract 96 from 64 to get -32.

$$-\frac{32}{27}$$

Factor

$$-\frac{32}{27} = -1\frac{5}{27} = -1.1851851851851851$$