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

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

Evaluate

$$-\frac{169}{2}=-84.5$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{2}-8\times 9+3-2^{2}\times 4$$

Multiply 8 and 9 to get 72.

$$\frac{1}{2}-72+3-2^{2}\times 4$$

Convert 72 to fraction \frac{144}{2}.

$$\frac{1}{2}-\frac{144}{2}+3-2^{2}\times 4$$

Since \frac{1}{2} and \frac{144}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-144}{2}+3-2^{2}\times 4$$

Subtract 144 from 1 to get -143.

$$-\frac{143}{2}+3-2^{2}\times 4$$

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

$$-\frac{143}{2}+\frac{6}{2}-2^{2}\times 4$$

Since -\frac{143}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{-143+6}{2}-2^{2}\times 4$$

Add -143 and 6 to get -137.

$$-\frac{137}{2}-2^{2}\times 4$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{137}{2}-4\times 4$$

Multiply 4 and 4 to get 16.

$$-\frac{137}{2}-16$$

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

$$-\frac{137}{2}-\frac{32}{2}$$

Since -\frac{137}{2} and \frac{32}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-137-32}{2}$$

Subtract 32 from -137 to get -169.

$$-\frac{169}{2}$$

Factor

$$-\frac{169}{2} = -84\frac{1}{2} = -84.5$$