Solve 3^{5}+3^{5}+3^{5}+3^{6}+3^{6}+3^{7}+3^{7}+3^8+3^8+3^9+3^9

$$3 ^ { 5 } + 3 ^ { 5 } + 3 ^ { 5 } + 3 ^ { 6 } + 3 ^ { 6 } + 3 ^ { 7 } + 3 ^ { 7 } + 3 ^ { 8 } + 3 ^ { 8 } + 3 ^ { 9 } + 3 ^ { 9 }$$

Evaluate

$$59049$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$243+3^{5}+3^{5}+3^{6}+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 5 and get 243.

$$243+243+3^{5}+3^{6}+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 243 and 243 to get 486.

$$486+3^{5}+3^{6}+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 5 and get 243.

$$486+243+3^{6}+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 486 and 243 to get 729.

$$729+3^{6}+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 6 and get 729.

$$729+729+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 729 and 729 to get 1458.

$$1458+3^{6}+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 6 and get 729.

$$1458+729+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 1458 and 729 to get 2187.

$$2187+3^{7}+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 7 and get 2187.

$$2187+2187+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 2187 and 2187 to get 4374.

$$4374+3^{7}+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 7 and get 2187.

$$4374+2187+3^{8}+3^{8}+3^{9}+3^{9}$$

Add 4374 and 2187 to get 6561.

$$6561+3^{8}+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 8 and get 6561.

$$6561+6561+3^{8}+3^{9}+3^{9}$$

Add 6561 and 6561 to get 13122.

$$13122+3^{8}+3^{9}+3^{9}$$

Calculate 3 to the power of 8 and get 6561.

$$13122+6561+3^{9}+3^{9}$$

Add 13122 and 6561 to get 19683.

$$19683+3^{9}+3^{9}$$

Calculate 3 to the power of 9 and get 19683.

$$19683+19683+3^{9}$$

Add 19683 and 19683 to get 39366.

$$39366+3^{9}$$

Calculate 3 to the power of 9 and get 19683.

$$39366+19683$$

Add 39366 and 19683 to get 59049.

$$59049$$

Factor

$$3^{10}$$