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

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

Evaluate

$$1150903825$$

Solution Steps

Multiply 1+4^{4} and 1+4^{4} to get \left(1+4^{4}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$\left(1+16\right)\left(1+4^{4}\right)^{2}\left(1+4^{5}\right)$$

Add 1 and 16 to get 17.

$$17\left(1+4^{4}\right)^{2}\left(1+4^{5}\right)$$

Calculate 4 to the power of 4 and get 256.

$$17\left(1+256\right)^{2}\left(1+4^{5}\right)$$

Add 1 and 256 to get 257.

$$17\times 257^{2}\left(1+4^{5}\right)$$

Calculate 257 to the power of 2 and get 66049.

$$17\times 66049\left(1+4^{5}\right)$$

Multiply 17 and 66049 to get 1122833.

$$1122833\left(1+4^{5}\right)$$

Calculate 4 to the power of 5 and get 1024.

$$1122833\left(1+1024\right)$$

Add 1 and 1024 to get 1025.

$$1122833\times 1025$$

Multiply 1122833 and 1025 to get 1150903825.

$$1150903825$$

Factor

$$5^{2}\times 17\times 41\times 257^{2}$$