Solve 2-2^3+3/3+3(-2)-3^2/6-2/3

$$\frac{ 2 { -2 }^{ 3 } +3 }{ 3 } + \frac{ 3(-2)- { 3 }^{ 2 } }{ 6 } - \frac{ 2 }{ 3 }$$

Evaluate

$$-\frac{15}{2}=-7.5$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$\frac{2\left(-8\right)+3}{3}+\frac{3\left(-2\right)-3^{2}}{6}-\frac{2}{3}$$

Multiply 2 and -8 to get -16.

$$\frac{-16+3}{3}+\frac{3\left(-2\right)-3^{2}}{6}-\frac{2}{3}$$

Add -16 and 3 to get -13.

$$\frac{-13}{3}+\frac{3\left(-2\right)-3^{2}}{6}-\frac{2}{3}$$

Fraction \frac{-13}{3} can be rewritten as -\frac{13}{3} by extracting the negative sign.

$$-\frac{13}{3}+\frac{3\left(-2\right)-3^{2}}{6}-\frac{2}{3}$$

Multiply 3 and -2 to get -6.

$$-\frac{13}{3}+\frac{-6-3^{2}}{6}-\frac{2}{3}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{13}{3}+\frac{-6-9}{6}-\frac{2}{3}$$

Subtract 9 from -6 to get -15.

$$-\frac{13}{3}+\frac{-15}{6}-\frac{2}{3}$$

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{13}{3}-\frac{5}{2}-\frac{2}{3}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{13}{3} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{26}{6}-\frac{15}{6}-\frac{2}{3}$$

Since -\frac{26}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26-15}{6}-\frac{2}{3}$$

Subtract 15 from -26 to get -41.

$$-\frac{41}{6}-\frac{2}{3}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{41}{6} and \frac{2}{3} to fractions with denominator 6.

$$-\frac{41}{6}-\frac{4}{6}$$

Since -\frac{41}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-41-4}{6}$$

Subtract 4 from -41 to get -45.

$$\frac{-45}{6}$$

Reduce the fraction \frac{-45}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{15}{2}$$

Factor

$$-\frac{15}{2} = -7\frac{1}{2} = -7.5$$