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

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

Evaluate

$$7458340731200206743290965315462933837376471534600406894271518333206278385070118304936174890400427803361511603255836101453412728095225302660486164829592084691481260792318781377495204074266435262941446554365063914765414217260588507120031686823003222742297563699265350215337206058336516628646003612927433551846968657326499008153319891789578832685947418212890625$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25^{\left(2^{2}\right)^{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$25^{4^{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$25^{4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$25^{256}$$

Calculate 25 to the power of 256 and get 7458340731200206743290965315462933837376471534600406894271518333206278385070118304936174890400427803361511603255836101453412728095225302660486164829592084691481260792318781377495204074266435262941446554365063914765414217260588507120031686823003222742297563699265350215337206058336516628646003612927433551846968657326499008153319891789578832685947418212890625.

$$7458340731200206743290965315462933837376471534600406894271518333206278385070118304936174890400427803361511603255836101453412728095225302660486164829592084691481260792318781377495204074266435262941446554365063914765414217260588507120031686823003222742297563699265350215337206058336516628646003612927433551846968657326499008153319891789578832685947418212890625$$

Factor

$$5^{512}$$