Let's analyze the pattern in the values given for the powers of 3:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Powers of 3} & \text{Value} \\
\hline
3^{-1} & \frac{1}{3} \\
\hline
3^0 & 1 \\
\hline
3^1 & 3 \\
\hline
3^2 & 9 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Analysis:
1. Starting with [tex]\(3^{-1}\)[/tex] to [tex]\(3^0\)[/tex]:
- [tex]\(3^{-1} = \frac{1}{3}\)[/tex]
- [tex]\(3^0 = 1\)[/tex]
To go from [tex]\(\frac{1}{3}\)[/tex] to 1, we can observe that:
[tex]\[
\frac{1}{3} \times 3 = 1
\][/tex]
2. Moving from [tex]\(3^0\)[/tex] to [tex]\(3^1\)[/tex]:
- [tex]\(3^0 = 1\)[/tex]
- [tex]\(3^1 = 3\)[/tex]
To go from 1 to 3, we see that:
[tex]\[
1 \times 3 = 3
\][/tex]
3. Continuing to [tex]\(3^1\)[/tex] to [tex]\(3^2\)[/tex]:
- [tex]\(3^1 = 3\)[/tex]
- [tex]\(3^2 = 9\)[/tex]
To go from 3 to 9, we notice:
[tex]\[
3 \times 3 = 9
\][/tex]
### Conclusion:
In each step, the value is obtained by multiplying the previous value by 3. Hence, the correct pattern as the exponents increase is:
[tex]\[
\text{multiply the previous value by 3}
\][/tex]
So, the correct choice here is:
- multiply the previous value by 3
