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