Solve frac{2008^{4}+2008^{3}*2-2008^2-2*2008+1-2008^4*2-2008^2}{2008^8+2007}

$$\frac { 2008 ^ { 4 } + 2008 ^ { 3 } \times 2 - 2008 ^ { 2 } - 2 \times 2008 + 1 - 2008 ^ { 4 } \times 2 - 2008 ^ { 2 } } { 2008 ^ { 8 } + 2007 }$$

Evaluate

$$-\frac{16241355399215}{264307610106229457699211223}\approx -6.144868622 \cdot 10^{-14}$$

Solution Steps

Calculate 2008 to the power of 4 and get 16257540100096.

$$\frac{16257540100096+2008^{3}\times 2-2008^{2}-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Calculate 2008 to the power of 3 and get 8096384512.

$$\frac{16257540100096+8096384512\times 2-2008^{2}-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Multiply 8096384512 and 2 to get 16192769024.

$$\frac{16257540100096+16192769024-2008^{2}-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Add 16257540100096 and 16192769024 to get 16273732869120.

$$\frac{16273732869120-2008^{2}-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Calculate 2008 to the power of 2 and get 4032064.

$$\frac{16273732869120-4032064-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Subtract 4032064 from 16273732869120 to get 16273728837056.

$$\frac{16273728837056-2\times 2008+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Multiply 2 and 2008 to get 4016.

$$\frac{16273728837056-4016+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Subtract 4016 from 16273728837056 to get 16273728833040.

$$\frac{16273728833040+1-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Add 16273728833040 and 1 to get 16273728833041.

$$\frac{16273728833041-2008^{4}\times 2-2008^{2}}{2008^{8}+2007}$$

Calculate 2008 to the power of 4 and get 16257540100096.

$$\frac{16273728833041-16257540100096\times 2-2008^{2}}{2008^{8}+2007}$$

Multiply 16257540100096 and 2 to get 32515080200192.

$$\frac{16273728833041-32515080200192-2008^{2}}{2008^{8}+2007}$$

Subtract 32515080200192 from 16273728833041 to get -16241351367151.

$$\frac{-16241351367151-2008^{2}}{2008^{8}+2007}$$

Calculate 2008 to the power of 2 and get 4032064.

$$\frac{-16241351367151-4032064}{2008^{8}+2007}$$

Subtract 4032064 from -16241351367151 to get -16241355399215.

$$\frac{-16241355399215}{2008^{8}+2007}$$

Calculate 2008 to the power of 8 and get 264307610106229457699209216.

$$\frac{-16241355399215}{264307610106229457699209216+2007}$$

Add 264307610106229457699209216 and 2007 to get 264307610106229457699211223.

$$\frac{-16241355399215}{264307610106229457699211223}$$

Fraction \frac{-16241355399215}{264307610106229457699211223} can be rewritten as -\frac{16241355399215}{264307610106229457699211223} by extracting the negative sign.

$$-\frac{16241355399215}{264307610106229457699211223}$$

Factor

$$-\frac{16241355399215}{264307610106229457699211223} = -6.144868622090502 \times 10^{-14}$$