Solve frac{4^{12}+4^{12}+4^{12}+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^4+4^4+4^4+4^4}

$$\frac { 4 ^ { 12 } + 4 ^ { 12 } + 4 ^ { 12 } + 4 ^ { 12 } + 4 ^ { 12 } + 4 ^ { 21 } + 4 ^ { 2 } + 4 ^ { 12 } } { 4 ^ { 4 } + 4 ^ { 4 } + 4 ^ { 4 } + 4 ^ { 4 } }$$

Evaluate

$$\frac{274884198401}{64}=4295065600.015625$$

Solution Steps

Calculate 4 to the power of 12 and get 16777216.

$$\frac{16777216+4^{12}+4^{12}+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{16777216+16777216+4^{12}+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 16777216 and 16777216 to get 33554432.

$$\frac{33554432+4^{12}+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{33554432+16777216+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 33554432 and 16777216 to get 50331648.

$$\frac{50331648+4^{12}+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{50331648+16777216+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 50331648 and 16777216 to get 67108864.

$$\frac{67108864+4^{12}+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{67108864+16777216+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 67108864 and 16777216 to get 83886080.

$$\frac{83886080+4^{21}+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 21 and get 4398046511104.

$$\frac{83886080+4398046511104+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 83886080 and 4398046511104 to get 4398130397184.

$$\frac{4398130397184+4^{2}+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{4398130397184+16+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 4398130397184 and 16 to get 4398130397200.

$$\frac{4398130397200+4^{12}}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 12 and get 16777216.

$$\frac{4398130397200+16777216}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Add 4398130397200 and 16777216 to get 4398147174416.

$$\frac{4398147174416}{4^{4}+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{4398147174416}{256+4^{4}+4^{4}+4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{4398147174416}{256+256+4^{4}+4^{4}}$$

Add 256 and 256 to get 512.

$$\frac{4398147174416}{512+4^{4}+4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{4398147174416}{512+256+4^{4}}$$

Add 512 and 256 to get 768.

$$\frac{4398147174416}{768+4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{4398147174416}{768+256}$$

Add 768 and 256 to get 1024.

$$\frac{4398147174416}{1024}$$

Reduce the fraction \frac{4398147174416}{1024} to lowest terms by extracting and canceling out 16.

$$\frac{274884198401}{64}$$

Factor

$$\frac{23 \cdot 78607 \cdot 152041}{2 ^ {6}} = 4295065600\frac{1}{64} = 4295065600.015625$$