Given a prime p, we show that every binomial coefficient in the pth row of Pascal’s triangle is divisible by p, unless we are talking about the entries of 1 on the far left and far right. We deduce this from a more general result, and deduce from it a property of the $p^{\text{th}}$ power map modulo $p$, otherwise known as the Frobenius endomorphism. That is, we prove that the Freshman’s Dream (that powers distribute over sums) is actually true for an exponent $p$ modulo $p$, even thought it is certainly not true in general.