Solve -4^2+5:10/5-3*(-1)/-(frac{1{3})^2+(-1/3)^2-12/3}-(-3)^2=

$$\frac { - 4 ^ { 2 } + 5 : \frac { 10 } { 5 } - 3 \cdot ( - 1 ) } { - ( \frac { 1 } { 3 } ) ^ { 2 } + ( - \frac { 1 } { 3 } ) ^ { 2 } - \frac { 12 } { 3 } } - ( - 3 ) ^ { 2 } =$$

Evaluate

$$-\frac{51}{8}=-6.375$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-16+\frac{5}{\frac{10}{5}}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Divide 5 by \frac{10}{5} by multiplying 5 by the reciprocal of \frac{10}{5}.

$$\frac{-16+\frac{5\times 5}{10}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Multiply 5 and 5 to get 25.

$$\frac{-16+\frac{25}{10}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{-16+\frac{5}{2}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Convert -16 to fraction -\frac{32}{2}.

$$\frac{-\frac{32}{2}+\frac{5}{2}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Since -\frac{32}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-32+5}{2}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Add -32 and 5 to get -27.

$$\frac{-\frac{27}{2}-3\left(-1\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Multiply 3 and -1 to get -3.

$$\frac{-\frac{27}{2}-\left(-3\right)}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

The opposite of -3 is 3.

$$\frac{-\frac{27}{2}+3}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{-\frac{27}{2}+\frac{6}{2}}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Since -\frac{27}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-27+6}{2}}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

Add -27 and 6 to get -21.

$$\frac{-\frac{21}{2}}{-\left(\frac{1}{3}\right)^{2}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

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

$$\frac{-\frac{21}{2}}{-\frac{1}{9}+\left(-\frac{1}{3}\right)^{2}-\frac{12}{3}}-\left(-3\right)^{2}$$

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

$$\frac{-\frac{21}{2}}{-\frac{1}{9}+\frac{1}{9}-\frac{12}{3}}-\left(-3\right)^{2}$$

Add -\frac{1}{9} and \frac{1}{9} to get 0.

$$\frac{-\frac{21}{2}}{-\frac{12}{3}}-\left(-3\right)^{2}$$

Divide 12 by 3 to get 4.

$$\frac{-\frac{21}{2}}{-4}-\left(-3\right)^{2}$$

Express \frac{-\frac{21}{2}}{-4} as a single fraction.

$$\frac{-21}{2\left(-4\right)}-\left(-3\right)^{2}$$

Multiply 2 and -4 to get -8.

$$\frac{-21}{-8}-\left(-3\right)^{2}$$

Fraction \frac{-21}{-8} can be simplified to \frac{21}{8} by removing the negative sign from both the numerator and the denominator.

$$\frac{21}{8}-\left(-3\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{21}{8}-9$$

Convert 9 to fraction \frac{72}{8}.

$$\frac{21}{8}-\frac{72}{8}$$

Since \frac{21}{8} and \frac{72}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-72}{8}$$

Subtract 72 from 21 to get -51.

$$-\frac{51}{8}$$

Factor

$$-\frac{51}{8} = -6\frac{3}{8} = -6.375$$