$E(X_n | X_m) = X_m \mu^{n-m}$ for $ m\leq n$ for branching process $X_n$

Question

Let $X_n$ be the size of the $n$th generation in an ordinary branching process with $X_0 = 1, E (X_1) = \mu$, and Var$(X_1) > 0$. It is claimed that for $m \leq n$

$$E(X_n | X_m) = X_m \mu^{n-m}$$ and $$E(X_nX_m | X_m) = X_m^2 \mu^{n-m}$$

I know that $E(X_n) = \mu^n$, but I don't understand the reasoning behind or the way of computing these conditional expectations. Any hint?