To express the product \((1/8)(1/8)(1/8)\) in exponential form, we first recognize that we are multiplying the same base, which is \(1/8\), a total of three times.
The expression can be rewritten as:
\[ (1/8)(1/8)(1/8) = (1/8)^3 \]
In this case, the base is \(1/8\) and it is raised to the power of \(3\). Therefore, the exponent in the exponential form of the expression is:
\[ \boxed{3} \]