Solve 1/2-2^33^2+3-2^24^2

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

Evaluate

$$-\frac{265}{2}=-132.5$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

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

Calculate 3 to the power of 2 and get 9.

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

Multiply 8 and 9 to get 72.

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

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

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

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

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

Subtract 144 from 1 to get -143.

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

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

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

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

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

Add -143 and 6 to get -137.

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 4 to the power of 2 and get 16.

$$-\frac{137}{2}-4\times 16$$

Multiply 4 and 16 to get 64.

$$-\frac{137}{2}-64$$

Convert 64 to fraction \frac{128}{2}.

$$-\frac{137}{2}-\frac{128}{2}$$

Since -\frac{137}{2} and \frac{128}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-137-128}{2}$$

Subtract 128 from -137 to get -265.

$$-\frac{265}{2}$$

Factor

$$-\frac{265}{2} = -132\frac{1}{2} = -132.5$$