Question 3
Given $x$, three operations suffice for $x^8$: $x^2=x\cdot x$, $x^4=x^2\cdot x^2$, $x^8=x^4\cdot x^4$. Five suffice for $x^{15}$: the same first three, then $x^{16}=x^8\cdot x^8$, $x^{15}=x^{16}\div x$. What is the minimum number of multiplications and divisions needed to find $x^{1000}$?