Solve (2)-6^2*(-1/2-7/18+5/6)+(-2)^2

$$( 2 ) - 6 ^ { 2 } \times ( - \frac { 1 } { 2 } - \frac { 7 } { 18 } + \frac { 5 } { 6 } ) + ( - 2 ) ^ { 2 }$$

Evaluate

$$8$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$2-36\left(-\frac{1}{2}-\frac{7}{18}+\frac{5}{6}\right)+\left(-2\right)^{2}$$

Least common multiple of 2 and 18 is 18. Convert -\frac{1}{2} and \frac{7}{18} to fractions with denominator 18.

$$2-36\left(-\frac{9}{18}-\frac{7}{18}+\frac{5}{6}\right)+\left(-2\right)^{2}$$

Since -\frac{9}{18} and \frac{7}{18} have the same denominator, subtract them by subtracting their numerators.

$$2-36\left(\frac{-9-7}{18}+\frac{5}{6}\right)+\left(-2\right)^{2}$$

Subtract 7 from -9 to get -16.

$$2-36\left(\frac{-16}{18}+\frac{5}{6}\right)+\left(-2\right)^{2}$$

Reduce the fraction \frac{-16}{18} to lowest terms by extracting and canceling out 2.

$$2-36\left(-\frac{8}{9}+\frac{5}{6}\right)+\left(-2\right)^{2}$$

Least common multiple of 9 and 6 is 18. Convert -\frac{8}{9} and \frac{5}{6} to fractions with denominator 18.

$$2-36\left(-\frac{16}{18}+\frac{15}{18}\right)+\left(-2\right)^{2}$$

Since -\frac{16}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$2-36\times \frac{-16+15}{18}+\left(-2\right)^{2}$$

Add -16 and 15 to get -1.

$$2-36\left(-\frac{1}{18}\right)+\left(-2\right)^{2}$$

Express 36\left(-\frac{1}{18}\right) as a single fraction.

$$2-\frac{36\left(-1\right)}{18}+\left(-2\right)^{2}$$

Multiply 36 and -1 to get -36.

$$2-\frac{-36}{18}+\left(-2\right)^{2}$$

Divide -36 by 18 to get -2.

$$2-\left(-2\right)+\left(-2\right)^{2}$$

The opposite of -2 is 2.

$$2+2+\left(-2\right)^{2}$$

Add 2 and 2 to get 4.

$$4+\left(-2\right)^{2}$$

Calculate -2 to the power of 2 and get 4.

$$4+4$$

Add 4 and 4 to get 8.

$$8$$

Factor

$$2^{3}$$