To multiply the numbers \(123456789123456789\) and \(987654321987654321\), we perform the multiplication directly as follows:

\[
123456789123456789 \times 987654321987654321
\]

Using a calculator or a computer to handle the large numbers, we compute the product to be:

\[
121932631356500531347203169112635269
\]

Therefore, the exact result of multiplying \(123456789123456789\) by \(987654321987654321\) is \(121932631356500531347203169112635269\).
