[tex]\displaystyle\\
125^{13}-124\times 5^{36}=\\\\
=\Big(5^3\Big)^{13}-124\times 5^{36}=\\\\
=5^{3\times13}-124\times 5^{36}=\\\\
=5^{39}-124\times 5^{36}=\\\\
=5^{36+3}-124\times 5^{36}=\\\\
=5^{36}\times5^{3}-124\times 5^{36}=\\\\
=5^{36}(5^{3}-124)=5^{36}(125-124)=5^{36}\times 1 = \boxed{\bf 5^{36}}
[/tex]
