Solve 2^{11}+2^{10}+2^{9}+2^{7}+2^6+2^5+2^3+2^2+2

$$2 ^ { 11 } + 2 ^ { 10 } + 2 ^ { 9 } + 2 ^ { 7 } + 2 ^ { 6 } + 2 ^ { 5 } + 2 ^ { 3 } + 2 ^ { 2 } + 2$$

Evaluate

$$3822$$

Solution Steps

Calculate 2 to the power of 11 and get 2048.

$$2048+2^{10}+2^{9}+2^{7}+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Calculate 2 to the power of 10 and get 1024.

$$2048+1024+2^{9}+2^{7}+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Add 2048 and 1024 to get 3072.

$$3072+2^{9}+2^{7}+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Calculate 2 to the power of 9 and get 512.

$$3072+512+2^{7}+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Add 3072 and 512 to get 3584.

$$3584+2^{7}+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Calculate 2 to the power of 7 and get 128.

$$3584+128+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Add 3584 and 128 to get 3712.

$$3712+2^{6}+2^{5}+2^{3}+2^{2}+2$$

Calculate 2 to the power of 6 and get 64.

$$3712+64+2^{5}+2^{3}+2^{2}+2$$

Add 3712 and 64 to get 3776.

$$3776+2^{5}+2^{3}+2^{2}+2$$

Calculate 2 to the power of 5 and get 32.

$$3776+32+2^{3}+2^{2}+2$$

Add 3776 and 32 to get 3808.

$$3808+2^{3}+2^{2}+2$$

Calculate 2 to the power of 3 and get 8.

$$3808+8+2^{2}+2$$

Add 3808 and 8 to get 3816.

$$3816+2^{2}+2$$

Calculate 2 to the power of 2 and get 4.

$$3816+4+2$$

Add 3816 and 4 to get 3820.

$$3820+2$$

Add 3820 and 2 to get 3822.

$$3822$$

Factor

$$2\times 3\times 7^{2}\times 13$$