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

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

Evaluate

$$0$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$3\times \frac{8}{27}-2\times \left(\frac{2}{3}\right)^{2}-3\times \frac{2}{3}+2$$

Express 3\times \frac{8}{27} as a single fraction.

$$\frac{3\times 8}{27}-2\times \left(\frac{2}{3}\right)^{2}-3\times \frac{2}{3}+2$$

Multiply 3 and 8 to get 24.

$$\frac{24}{27}-2\times \left(\frac{2}{3}\right)^{2}-3\times \frac{2}{3}+2$$

Reduce the fraction \frac{24}{27} to lowest terms by extracting and canceling out 3.

$$\frac{8}{9}-2\times \left(\frac{2}{3}\right)^{2}-3\times \frac{2}{3}+2$$

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

$$\frac{8}{9}-2\times \frac{4}{9}-3\times \frac{2}{3}+2$$

Express 2\times \frac{4}{9} as a single fraction.

$$\frac{8}{9}-\frac{2\times 4}{9}-3\times \frac{2}{3}+2$$

Multiply 2 and 4 to get 8.

$$\frac{8}{9}-\frac{8}{9}-3\times \frac{2}{3}+2$$

Subtract \frac{8}{9} from \frac{8}{9} to get 0.

$$0-3\times \frac{2}{3}+2$$

Cancel out 3 and 3.

$$0-2+2$$

Subtract 2 from 0 to get -2.

$$-2+2$$

Add -2 and 2 to get 0.

$$0$$

Factor

$$0$$