Solve {left({left(left(left(left(5^2right)^2right)^2right)^2right)}^2right)}^2

$${ \left( { \left( { \left( { \left( { \left( { 5 }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$542101086242752217003726400434970855712890625$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(\left(\left(5^{8}\right)^{2}\right)^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

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

To raise a power to another power, multiply the exponents. Multiply 16 and 2 to get 32.

$$\left(5^{32}\right)^{2}$$

Calculate 5 to the power of 32 and get 23283064365386962890625.

$$23283064365386962890625^{2}$$

Calculate 23283064365386962890625 to the power of 2 and get 542101086242752217003726400434970855712890625.

$$542101086242752217003726400434970855712890625$$

Factor

$$5^{64}$$