The problem of embedding an interconnection network $G$ into another interconnection network $H$ arises when algorithms from parallel machine $G$ are simulated onto parallel machine $H$. In this paper, we present efficient solutions to this problem when $G$ is a complete $k$-ary tree and $H$ is a boolean hypercube. In particular we describe an embedding of a complete ternary tree (i.e. $k=3$) into a hypercube such that it achieves a dilation of $3$ and an expansion of $O(1)$. We also describe efficient embeddings of $k$-ary trees into hypercubes when $k=2^p*3^q$ for some $p,q\ge 0$ such that the embeddings achieve $O(1)$ dilation and $O(1)$ expansion.