Solve 2^3/6-2(2)^2+5(2)+1

$$\frac { 2 ^ { 3 } } { 6 } - 2 ( 2 ) ^ { 2 } + 5 ( 2 ) + 1$$

Evaluate

$$\frac{13}{3}\approx 4.333333333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{2^{3}}{6}-2^{3}+5\times 2+1$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{6}-2^{3}+5\times 2+1$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}-2^{3}+5\times 2+1$$

Calculate 2 to the power of 3 and get 8.

$$\frac{4}{3}-8+5\times 2+1$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{4}{3}-\frac{24}{3}+5\times 2+1$$

Since \frac{4}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-24}{3}+5\times 2+1$$

Subtract 24 from 4 to get -20.

$$-\frac{20}{3}+5\times 2+1$$

Multiply 5 and 2 to get 10.

$$-\frac{20}{3}+10+1$$

Convert 10 to fraction \frac{30}{3}.

$$-\frac{20}{3}+\frac{30}{3}+1$$

Since -\frac{20}{3} and \frac{30}{3} have the same denominator, add them by adding their numerators.

$$\frac{-20+30}{3}+1$$

Add -20 and 30 to get 10.

$$\frac{10}{3}+1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{10}{3}+\frac{3}{3}$$

Since \frac{10}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{3}$$

Add 10 and 3 to get 13.

$$\frac{13}{3}$$

Factor

$$\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333$$