Solve frac{2^{16}-2}{8^4+8^3+8^2+8^1+1}

$$\frac { 2 ^ { 16 } - 2 } { 8 ^ { 4 } + 8 ^ { 3 } + 8 ^ { 2 } + 8 ^ { 1 } + 1 }$$

Evaluate

$$14$$

Solution Steps

Calculate 2 to the power of 16 and get 65536.

$$\frac{65536-2}{8^{4}+8^{3}+8^{2}+8^{1}+1}$$

Subtract 2 from 65536 to get 65534.

$$\frac{65534}{8^{4}+8^{3}+8^{2}+8^{1}+1}$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{65534}{4096+8^{3}+8^{2}+8^{1}+1}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{65534}{4096+512+8^{2}+8^{1}+1}$$

Add 4096 and 512 to get 4608.

$$\frac{65534}{4608+8^{2}+8^{1}+1}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{65534}{4608+64+8^{1}+1}$$

Add 4608 and 64 to get 4672.

$$\frac{65534}{4672+8^{1}+1}$$

Calculate 8 to the power of 1 and get 8.

$$\frac{65534}{4672+8+1}$$

Add 4672 and 8 to get 4680.

$$\frac{65534}{4680+1}$$

Add 4680 and 1 to get 4681.

$$\frac{65534}{4681}$$

Divide 65534 by 4681 to get 14.

$$14$$

Factor

$$2\times 7$$