Solve =2^8/2-1/2+2^14-12^8+1

$$= \frac { 2 ^ { 8 } } { 2 } - \frac { 1 } { 2 } + 2 ^ { 14 } - 12 ^ { 8 } + 1$$

Evaluate

$$-\frac{859930367}{2}=-429965183.5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 8 to get 7.

$$2^{7}-\frac{1}{2}+2^{14}-12^{8}+1$$

Calculate 2 to the power of 7 and get 128.

$$128-\frac{1}{2}+2^{14}-12^{8}+1$$

Convert 128 to fraction \frac{256}{2}.

$$\frac{256}{2}-\frac{1}{2}+2^{14}-12^{8}+1$$

Since \frac{256}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{256-1}{2}+2^{14}-12^{8}+1$$

Subtract 1 from 256 to get 255.

$$\frac{255}{2}+2^{14}-12^{8}+1$$

Calculate 2 to the power of 14 and get 16384.

$$\frac{255}{2}+16384-12^{8}+1$$

Convert 16384 to fraction \frac{32768}{2}.

$$\frac{255}{2}+\frac{32768}{2}-12^{8}+1$$

Since \frac{255}{2} and \frac{32768}{2} have the same denominator, add them by adding their numerators.

$$\frac{255+32768}{2}-12^{8}+1$$

Add 255 and 32768 to get 33023.

$$\frac{33023}{2}-12^{8}+1$$

Calculate 12 to the power of 8 and get 429981696.

$$\frac{33023}{2}-429981696+1$$

Convert 429981696 to fraction \frac{859963392}{2}.

$$\frac{33023}{2}-\frac{859963392}{2}+1$$

Since \frac{33023}{2} and \frac{859963392}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33023-859963392}{2}+1$$

Subtract 859963392 from 33023 to get -859930369.

$$-\frac{859930369}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{859930369}{2}+\frac{2}{2}$$

Since -\frac{859930369}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-859930369+2}{2}$$

Add -859930369 and 2 to get -859930367.

$$-\frac{859930367}{2}$$

Factor

$$-\frac{859930367}{2} = -429965183\frac{1}{2} = -429965183.5$$