First compute this pair: $\underbrace{a*a}*a*a*a*a*a*a$

Let the result be $x$.

Re-write the equation: $x*x*x*x$

Repeat what you did above. $\underbrace{x*x}*x*x$

Let this result be $y$

Re write: $y*y$

Multiply just this.

Total multiplications needed = 3.