Solve 1^2/3-4^2/2+6^2/6

$$\frac { 1 ^ { 2 } } { 3 } - \frac { 4 ^ { 2 } } { 2 } + \frac { 6 ^ { 2 } } { 6 }$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

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

$$\frac{1^{2}}{3}-\frac{4^{2}}{2}+6^{1}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{3}-\frac{4^{2}}{2}+6^{1}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{3}-\frac{16}{2}+6^{1}$$

Divide 16 by 2 to get 8.

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

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

$$\frac{1}{3}-\frac{24}{3}+6^{1}$$

Since \frac{1}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-24}{3}+6^{1}$$

Subtract 24 from 1 to get -23.

$$-\frac{23}{3}+6^{1}$$

Calculate 6 to the power of 1 and get 6.

$$-\frac{23}{3}+6$$

Convert 6 to fraction \frac{18}{3}.

$$-\frac{23}{3}+\frac{18}{3}$$

Since -\frac{23}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$\frac{-23+18}{3}$$

Add -23 and 18 to get -5.

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

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$