Solve -4^2+frac{5/frac{10{5}}-3*(-1)}{-{left(1/3right)}^2+{left(-1/3right)}^2-1^2/3}--3^2

$$\frac{ - { 4 }^{ 2 } + \frac{ 5 }{ \frac{ 10 }{ 5 } } -3 \times (-1) }{ - { \left( \frac{ 1 }{ 3 } \right) }^{ 2 } + { \left(- \frac{ 1 }{ 3 } \right) }^{ 2 } - \frac{ { 1 }^{ 2 } }{ 3 } } - { -3 }^{ 2 }$$

Evaluate

$$\frac{45}{2}=22.5$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

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

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

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

Multiply 5 and 5 to get 25.

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

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

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

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

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

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

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

Add -32 and 5 to get -27.

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

Multiply 3 and -1 to get -3.

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

The opposite of -3 is 3.

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

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

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

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

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

Add -27 and 6 to get -21.

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

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

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

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

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

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

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

Calculate 1 to the power of 2 and get 1.

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

Divide -\frac{21}{2} by -\frac{1}{3} by multiplying -\frac{21}{2} by the reciprocal of -\frac{1}{3}.

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

Express -\frac{21}{2}\left(-3\right) as a single fraction.

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

Multiply -21 and -3 to get 63.

$$\frac{63}{2}-\left(-3\right)^{2}$$

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

$$\frac{63}{2}-9$$

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

$$\frac{63}{2}-\frac{18}{2}$$

Since \frac{63}{2} and \frac{18}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-18}{2}$$

Subtract 18 from 63 to get 45.

$$\frac{45}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2} = 22\frac{1}{2} = 22.5$$