Question

How do you simplfy `(p^(1/5) p^(7/10) p^ (1/2) )/( (p^3)^ (-1/5)`?

Answer 1

First, let's condense this statement.

`(p^(1/5)p^(7/10)p^(1/2))/((p^3)^(-1/5)) = (p^(1/5+7/10+1/2))/p^((-3)/5) = (p^(2/10+7/10+5/10))/p^((-6)/10) = p^(14/10)/p^((-6)/10)`

We're almost done. See that negative exponent on the bottom? We can turn that into a positive exponent on the top, thanks to the way that exponents are defined.

`p^(14/10)/p^((-6)/10) = p^(14/10+6/10) = p^(20/10) = p^2`

Final Answer