Solve sqrt[4]{5(3^{2}+2^{2})[3^{4}+2^4](3^8+2^8)}+4^8

$$\sqrt[ 4 ] { 5 ( 3 ^ { 2 } + 2 ^ { 2 } ) [ 3 ^ { 4 } + 2 ^ { 4 } ] ( 3 ^ { 8 } + 2 ^ { 8 } ) } + 4 ^ { 8 }$$

Evaluate

$$\sqrt[4]{42981185}+65536\approx 65616.969152997$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt[4]{5\left(9+2^{2}\right)\left(3^{4}+2^{4}\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt[4]{5\left(9+4\right)\left(3^{4}+2^{4}\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Add 9 and 4 to get 13.

$$\sqrt[4]{5\times 13\left(3^{4}+2^{4}\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Multiply 5 and 13 to get 65.

$$\sqrt[4]{65\left(3^{4}+2^{4}\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Calculate 3 to the power of 4 and get 81.

$$\sqrt[4]{65\left(81+2^{4}\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt[4]{65\left(81+16\right)\left(3^{8}+2^{8}\right)}+4^{8}$$

Add 81 and 16 to get 97.

$$\sqrt[4]{65\times 97\left(3^{8}+2^{8}\right)}+4^{8}$$

Multiply 65 and 97 to get 6305.

$$\sqrt[4]{6305\left(3^{8}+2^{8}\right)}+4^{8}$$

Calculate 3 to the power of 8 and get 6561.

$$\sqrt[4]{6305\left(6561+2^{8}\right)}+4^{8}$$

Calculate 2 to the power of 8 and get 256.

$$\sqrt[4]{6305\left(6561+256\right)}+4^{8}$$

Add 6561 and 256 to get 6817.

$$\sqrt[4]{6305\times 6817}+4^{8}$$

Multiply 6305 and 6817 to get 42981185.

$$\sqrt[4]{42981185}+4^{8}$$

Calculate 4 to the power of 8 and get 65536.

$$\sqrt[4]{42981185}+65536$$