remember
[tex](x^a)^b=x^{ab}[/tex]
and
so maybe we want to find a and b such that [tex]a^2=b^3=5^{24}[/tex]
24/2=12, so 12*2=24 so [tex]5^{24}=5^{12*2}=(5^{12})^2[/tex]
24/3=8, so 8*3=24 so [tex]5^{24}=5^{8*3}=(5^8)^3[/tex]
so
[tex](5^{12})^2=(5^8)^3=5^{24}[/tex]
I think those are in factored index form
