Answer :
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]
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]
