Solve frac{2^{98}+4^{50}-8^34}{2^99-32^20+2^101}

$$\frac { 2 ^ { 98 } + 4 ^ { 50 } - 8 ^ { 34 } } { 2 ^ { 99 } - 32 ^ { 20 } + 2 ^ { 101 } }$$

Evaluate

$$-\frac{11}{6}\approx -1.833333333$$

Solution Steps

Calculate 2 to the power of 98 and get 316912650057057350374175801344.

$$\frac{316912650057057350374175801344+4^{50}-8^{34}}{2^{99}-32^{20}+2^{101}}$$

Calculate 4 to the power of 50 and get 1267650600228229401496703205376.

$$\frac{316912650057057350374175801344+1267650600228229401496703205376-8^{34}}{2^{99}-32^{20}+2^{101}}$$

Add 316912650057057350374175801344 and 1267650600228229401496703205376 to get 1584563250285286751870879006720.

$$\frac{1584563250285286751870879006720-8^{34}}{2^{99}-32^{20}+2^{101}}$$

Calculate 8 to the power of 34 and get 5070602400912917605986812821504.

$$\frac{1584563250285286751870879006720-5070602400912917605986812821504}{2^{99}-32^{20}+2^{101}}$$

Subtract 5070602400912917605986812821504 from 1584563250285286751870879006720 to get -3486039150627630854115933814784.

$$\frac{-3486039150627630854115933814784}{2^{99}-32^{20}+2^{101}}$$

Calculate 2 to the power of 99 and get 633825300114114700748351602688.

$$\frac{-3486039150627630854115933814784}{633825300114114700748351602688-32^{20}+2^{101}}$$

Calculate 32 to the power of 20 and get 1267650600228229401496703205376.

$$\frac{-3486039150627630854115933814784}{633825300114114700748351602688-1267650600228229401496703205376+2^{101}}$$

Subtract 1267650600228229401496703205376 from 633825300114114700748351602688 to get -633825300114114700748351602688.

$$\frac{-3486039150627630854115933814784}{-633825300114114700748351602688+2^{101}}$$

Calculate 2 to the power of 101 and get 2535301200456458802993406410752.

$$\frac{-3486039150627630854115933814784}{-633825300114114700748351602688+2535301200456458802993406410752}$$

Add -633825300114114700748351602688 and 2535301200456458802993406410752 to get 1901475900342344102245054808064.

$$\frac{-3486039150627630854115933814784}{1901475900342344102245054808064}$$

Reduce the fraction \frac{-3486039150627630854115933814784}{1901475900342344102245054808064} to lowest terms by extracting and canceling out 316912650057057350374175801344.

$$-\frac{11}{6}$$

Factor

$$-\frac{11}{6} = -1\frac{5}{6} = -1.8333333333333333$$