Solve 3^3/3+3^2/2-18-1

$$\frac{ { 3 }^{ 3 } }{ 3 } + \frac{ { 3 }^{ 2 } }{ 2 } -18-1$$

Evaluate

$$-\frac{11}{2}=-5.5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$3^{2}+\frac{3^{2}}{2}-18-1$$

Calculate 3 to the power of 2 and get 9.

$$9+\frac{3^{2}}{2}-18-1$$

Calculate 3 to the power of 2 and get 9.

$$9+\frac{9}{2}-18-1$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{18}{2}+\frac{9}{2}-18-1$$

Since \frac{18}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{18+9}{2}-18-1$$

Add 18 and 9 to get 27.

$$\frac{27}{2}-18-1$$

Convert 18 to fraction \frac{36}{2}.

$$\frac{27}{2}-\frac{36}{2}-1$$

Since \frac{27}{2} and \frac{36}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-36}{2}-1$$

Subtract 36 from 27 to get -9.

$$-\frac{9}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{9}{2}-\frac{2}{2}$$

Since -\frac{9}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-2}{2}$$

Subtract 2 from -9 to get -11.

$$-\frac{11}{2}$$

Factor

$$-\frac{11}{2} = -5\frac{1}{2} = -5.5$$