Let's carefully evaluate each of the expressions in the table and insert the appropriate values step-by-step.
1. In the top left cell, we have 2:
[tex]\[
\text{Value in the top left cell: } 2
\][/tex]
2. For the middle cell of the first row (which will be denoted as A), we compute [tex]\( (-3)^3 \)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
So, place -27 in the middle cell of the first row.
3. In the bottom left cell, we have [tex]\( (-1)^3 \)[/tex]:
[tex]\[
(-1)^3 = -1
\][/tex]
Therefore, place -1 in the bottom left cell.
4. In the bottom middle cell, we have -1 (it is already provided).
5. Finally, in the bottom right cell, we compute [tex]\( (-1)^{10} \)[/tex]:
[tex]\[
(-1)^{10} = 1
\][/tex]
So, place 1 in the bottom right cell.
After placing all these values, the complete table looks like this:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
2 & -27 & 2 \\
\hline
-1 & -1 & 1 \\
\hline
\end{tabular}
\][/tex]
Thus, the detailed step-by-step solution results in the following filled table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
2 & \hspace{10pt} & -27 \\
\hline
\hspace{10pt} & -27 & \hspace{10pt} \\
\hline
-1 & -1 & 1 \\
\hline
\end{tabular}
\][/tex]
