Help understanding solution to problem involving roots

I have a problem:

ux^a=x

The solution shows:

ux^a=x;x^a-1=1/u;x=(1/u)^1/(a-1)

I understand everything except how they got the a-1 exponent on x in the first step. Could someone help me understand better?

Thanks!

The a-1 exponent comes from divind both sides by x and then simplifying using the division exponent rule x^a/x = x^a-1

Is that right?