Solve frac{8^{5}+28^{4}+3^{3}+8^2+8^3+6}{(3+1)^2(3^2+1)}

$$\frac { 8 ^ { 5 } + 28 ^ { 4 } + 3 ^ { 3 } + 8 ^ { 2 } + 8 ^ { 3 } + 6 } { ( 3 + 1 ) ^ { 2 } ( 3 ^ { 2 } + 1 ) }$$

Evaluate

$$\frac{648033}{160}=4050.20625$$

Solution Steps

Calculate 8 to the power of 5 and get 32768.

$$\frac{32768+28^{4}+3^{3}+8^{2}+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Calculate 28 to the power of 4 and get 614656.

$$\frac{32768+614656+3^{3}+8^{2}+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 32768 and 614656 to get 647424.

$$\frac{647424+3^{3}+8^{2}+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{647424+27+8^{2}+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 647424 and 27 to get 647451.

$$\frac{647451+8^{2}+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{647451+64+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 647451 and 64 to get 647515.

$$\frac{647515+8^{3}+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{647515+512+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 647515 and 512 to get 648027.

$$\frac{648027+6}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 648027 and 6 to get 648033.

$$\frac{648033}{\left(3+1\right)^{2}\left(3^{2}+1\right)}$$

Add 3 and 1 to get 4.

$$\frac{648033}{4^{2}\left(3^{2}+1\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{648033}{16\left(3^{2}+1\right)}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{648033}{16\left(9+1\right)}$$

Add 9 and 1 to get 10.

$$\frac{648033}{16\times 10}$$

Multiply 16 and 10 to get 160.

$$\frac{648033}{160}$$

Factor

$$\frac{3 \cdot 19 \cdot 11369}{2 ^ {5} \cdot 5} = 4050\frac{33}{160} = 4050.20625$$