Solve sqrt[32]{1+80(9^2+1)(9^4+1)(9^8+1)}

$$\sqrt[ 32 ] { 1 + 80 ( 9 ^ { 2 } + 1 ) ( 9 ^ { 4 } + 1 ) ( 9 ^ { 8 } + 1 ) }$$

Evaluate

$$3$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\sqrt[32]{1+80\left(81+1\right)\left(9^{4}+1\right)\left(9^{8}+1\right)}$$

Add 81 and 1 to get 82.

$$\sqrt[32]{1+80\times 82\left(9^{4}+1\right)\left(9^{8}+1\right)}$$

Multiply 80 and 82 to get 6560.

$$\sqrt[32]{1+6560\left(9^{4}+1\right)\left(9^{8}+1\right)}$$

Calculate 9 to the power of 4 and get 6561.

$$\sqrt[32]{1+6560\left(6561+1\right)\left(9^{8}+1\right)}$$

Add 6561 and 1 to get 6562.

$$\sqrt[32]{1+6560\times 6562\left(9^{8}+1\right)}$$

Multiply 6560 and 6562 to get 43046720.

$$\sqrt[32]{1+43046720\left(9^{8}+1\right)}$$

Calculate 9 to the power of 8 and get 43046721.

$$\sqrt[32]{1+43046720\left(43046721+1\right)}$$

Add 43046721 and 1 to get 43046722.

$$\sqrt[32]{1+43046720\times 43046722}$$

Multiply 43046720 and 43046722 to get 1853020188851840.

$$\sqrt[32]{1+1853020188851840}$$

Add 1 and 1853020188851840 to get 1853020188851841.

$$\sqrt[32]{1853020188851841}$$

Calculate \sqrt[32]{1853020188851841} and get 3.

$$3$$

Factor

$$3$$