To compute \( 987654321^2 \), we need to perform the multiplication:

\[
987654321 \times 987654321
\]

Carrying out the multiplication step-by-step:

1. Write the numbers in the traditional multiplication format:

    \[
    \begin{array}{c}
    \ \ \ \ \ \ \ \ \ 987654321 \\
    \ \ \ \ \times \ 987654321 \\
    \hline
    \end{array}
    \]

2. Perform the multiplication by distributing each digit of the multiplier (\(987654321\)) over each digit of the multiplicand (\(987654321\)), starting from the rightmost digit.

This method is lengthy, so for brevity, I will provide you directly with the end result of this multiplication:

\[
987654321 \times 987654321 = 975461057789971041
\]

Thus, the exact square of \( 987654321 \) is \( 975461057789971041 \).
