Sure! Let's fill in the exponential forms for each product and expanded form in the table.
[tex]\[
\begin{tabular}{|l|c|l|}
\hline
Product & Expanded Form & Exponential Form \\
\hline
$3^2 \cdot 3^3$ & $(3 \cdot 3) \cdot(3 \cdot 3 \cdot 3)$ & $3^5$ \\
\hline
$5^1 \cdot 5^2$ & $(5) \cdot(5 \cdot 5)$ & $5^3$ \\
\hline
$8^3 \cdot 8^4$ & $(8 \cdot 8 \cdot 8) \cdot(8 \cdot 8 \cdot 8 \cdot 8)$ & $8^7$ \\
\hline
$7^6 \cdot 7^2$ & $(7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7) \cdot(7 \cdot 7)$ & $7^8$ \\
\hline
\end{tabular}
\][/tex]
Here's the detailed breakdown for each expression:
1. For [tex]\(3^2 \cdot 3^3\)[/tex]:
- Expanded form: [tex]\((3 \cdot 3) \cdot(3 \cdot 3 \cdot 3)\)[/tex]
- Exponential form: [tex]\(3^5\)[/tex]
2. For [tex]\(5^1 \cdot 5^2\)[/tex]:
- Expanded form: [tex]\((5) \cdot(5 \cdot 5)\)[/tex]
- Exponential form: [tex]\(5^3\)[/tex]
3. For [tex]\(8^3 \cdot 8^4\)[/tex]:
- Expanded form: [tex]\((8 \cdot 8 \cdot 8) \cdot(8 \cdot 8 \cdot 8 \cdot 8)\)[/tex]
- Exponential form: [tex]\(8^7\)[/tex]
4. For [tex]\(7^6 \cdot 7^2\)[/tex]:
- Expanded form: [tex]\((7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7) \cdot(7 \cdot 7)\)[/tex]
- Exponential form: [tex]\(7^8\)[/tex]
The table is now correctly filled with the exponential expressions for each product and expanded form.
