This comes from Jacobson's Basic Algebra I, Exercise 4 of Section 1.4, found on page 42. I don't understand the following problem.
For a given binary composition define a simple product of the sequence of elements $a_1,a_2,\dots,a_n$ inductively as either $a_1u$ where $u$ is a simple product of $a_2,\dots,a_n$ or as $va_n$ where $v$ is a simple product of $a_1,\dots,a_{n-1}$. Show that any product of $\geq 2^r$ elements can be written as a simple product of $r$ elements (which are themselves products).
I thought about approaching this by induction on $r$. But then for $r=1$, it seems to ask that any product of $\geq 2$ elements can be written as a simple product of $1$ element, which sounds unusual to me. The inductive definition given doesn't make sense to me, is there a better way to approach this problem?