Solve (-1/3)^3-(-1/3)^2+1/3+a

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

Evaluate

$$a = \frac{5}{27} = 0.18518518518518517$$

Solution Steps

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$-\frac{1}{27}-\left(-\frac{1}{3}\right)^{2}+\frac{1}{3}+a$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$-\frac{1}{27}-\frac{1}{9}+\frac{1}{3}+a$$

Least common multiple of 27 and 9 is 27. Convert -\frac{1}{27} and \frac{1}{9} to fractions with denominator 27.

$$-\frac{1}{27}-\frac{3}{27}+\frac{1}{3}+a$$

Since -\frac{1}{27} and \frac{3}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-3}{27}+\frac{1}{3}+a$$

Subtract 3 from -1 to get -4.

$$-\frac{4}{27}+\frac{1}{3}+a$$

Least common multiple of 27 and 3 is 27. Convert -\frac{4}{27} and \frac{1}{3} to fractions with denominator 27.

$$-\frac{4}{27}+\frac{9}{27}+a$$

Since -\frac{4}{27} and \frac{9}{27} have the same denominator, add them by adding their numerators.

$$\frac{-4+9}{27}+a$$

Add -4 and 9 to get 5.

$$\frac{5}{27}+a$$

Factor

$$\frac{27a+5}{27}$$

Solution Steps

Factor out \frac{1}{27}.

$$\frac{5+27a}{27}$$

Consider -1-3+9+27a. Multiply and combine like terms.

$$27a+5$$

Rewrite the complete factored expression.

$$\frac{27a+5}{27}$$