An algebra problem by Juliet Hanson

5^5000^0 should be properly evaluated as 5^(5000^0).5000^0 =1.Therefore 5^5000^0=5^1=5

$\large{5^{{5000}^0}=5^1=\boxed{5}}$

we should know the different between( a^{b})^{c} and a^{b}^{c }to answer this problem.i wanna explain it throw an example:

example1)if we have (2^{3})^{2} then at first we have to find the answer of 2^{3} =8 then find the answer of 8^{2} = 64

exaple2)But if we have 2^{3}^{2} then at first we have to find the answer of3^{2}=9 and then find the answer of 2^{9}=512

this problem is like example2: at first we have to find the answer of5000^{0}=1 and then find the answer of 5^{1}=5