Question

What are the factors of 5^24 that are both square and cube. Leave answer In factorised index form

Answer 1

Remember
$(x^a)^b=x^{ab}$
and

so maybe we want to find a and b such that $a^2=b^3=5^{24}$

24/2=12, so 12*2=24 so $5^{24}=5^{12*2}=(5^{12})^2$
24/3=8, so 8*3=24 so $5^{24}=5^{8*3}=(5^8)^3$
so
$(5^{12})^2=(5^8)^3=5^{24}$

I think those are in factored index form