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How to simplify expression with fractional exponents?

Is there a way to have Sage recognize that e^(2/3) times e^(1/3) in the below will simplify to just the variable e. Is there a type that can handle this? Obviously using a PolynomialRing in the code below won't work.

R.<a,e> = PolynomialRing(QQ)
p1 = (a+e^(1/3))
p2 = e^(2/3)