Solve =2^{1}+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^9+2^11+2^14+2^15

$$= 2 ^ { 1 } + 2 ^ { 2 } + 2 ^ { 3 } + 2 ^ { 4 } + 2 ^ { 5 } + 2 ^ { 6 } + 2 ^ { 7 } + 2 ^ { 9 } + 2 ^ { 11 } + 2 ^ { 14 } + 2 ^ { 15 }$$

Evaluate

$$51966$$

Solution Steps

Calculate 2 to the power of 1 and get 2.

$$2+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 2 and get 4.

$$2+4+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 2 and 4 to get 6.

$$6+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 3 and get 8.

$$6+8+2^{4}+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 6 and 8 to get 14.

$$14+2^{4}+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 4 and get 16.

$$14+16+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 14 and 16 to get 30.

$$30+2^{5}+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 5 and get 32.

$$30+32+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 30 and 32 to get 62.

$$62+2^{6}+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 6 and get 64.

$$62+64+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 62 and 64 to get 126.

$$126+2^{7}+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 7 and get 128.

$$126+128+2^{9}+2^{11}+2^{14}+2^{15}$$

Add 126 and 128 to get 254.

$$254+2^{9}+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 9 and get 512.

$$254+512+2^{11}+2^{14}+2^{15}$$

Add 254 and 512 to get 766.

$$766+2^{11}+2^{14}+2^{15}$$

Calculate 2 to the power of 11 and get 2048.

$$766+2048+2^{14}+2^{15}$$

Add 766 and 2048 to get 2814.

$$2814+2^{14}+2^{15}$$

Calculate 2 to the power of 14 and get 16384.

$$2814+16384+2^{15}$$

Add 2814 and 16384 to get 19198.

$$19198+2^{15}$$

Calculate 2 to the power of 15 and get 32768.

$$19198+32768$$

Add 19198 and 32768 to get 51966.

$$51966$$

Factor

$$2\times 3^{2}\times 2887$$