Solve (5+1)(5^2+1)(5^4^+1)(5^8+1)

$$(5+1)( { 5 }^{ 2 } +1)( { 5 }^{ { 4 }^{ } } +1)( { 5 }^{ 8 } +1)$$

Evaluate

$$38146972656$$

Solution Steps

Add 5 and 1 to get 6.

$$6\left(5^{2}+1\right)\left(5^{4^{1}}+1\right)\left(5^{8}+1\right)$$

Calculate 5 to the power of 2 and get 25.

$$6\left(25+1\right)\left(5^{4^{1}}+1\right)\left(5^{8}+1\right)$$

Add 25 and 1 to get 26.

$$6\times 26\left(5^{4^{1}}+1\right)\left(5^{8}+1\right)$$

Multiply 6 and 26 to get 156.

$$156\left(5^{4^{1}}+1\right)\left(5^{8}+1\right)$$

Calculate 4 to the power of 1 and get 4.

$$156\left(5^{4}+1\right)\left(5^{8}+1\right)$$

Calculate 5 to the power of 4 and get 625.

$$156\left(625+1\right)\left(5^{8}+1\right)$$

Add 625 and 1 to get 626.

$$156\times 626\left(5^{8}+1\right)$$

Multiply 156 and 626 to get 97656.

$$97656\left(5^{8}+1\right)$$

Calculate 5 to the power of 8 and get 390625.

$$97656\left(390625+1\right)$$

Add 390625 and 1 to get 390626.

$$97656\times 390626$$

Multiply 97656 and 390626 to get 38146972656.

$$38146972656$$

Factor

$$2^{4}\times 3\times 13\times 17\times 313\times 11489$$