To find the pattern as the exponents of 5 decrease, let's examine the provided values.
The table given is:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Powers of 5} & \text{Value} \\
\hline
5^3 & 125 \\
\hline
5^2 & 25 \\
\hline
5^1 & 5 \\
\hline
5^0 & 1 \\
\hline
5^{-1} & \frac{1}{5} \\
\hline
5^{-2} & \frac{1}{25} \\
\hline
\end{array}
\][/tex]
As we observe the values in the table:
- From [tex]\(5^3 = 125\)[/tex] to [tex]\(5^2 = 25\)[/tex], how do we get from 125 to 25? We divide 125 by 5.
- From [tex]\(5^2 = 25\)[/tex] to [tex]\(5^1 = 5\)[/tex], how do we get from 25 to 5? We divide 25 by 5.
- From [tex]\(5^1 = 5\)[/tex] to [tex]\(5^0 = 1\)[/tex], how do we get from 5 to 1? We divide 5 by 5.
- From [tex]\(5^0 = 1\)[/tex] to [tex]\(5^{-1} = \frac{1}{5}\)[/tex], how do we get from 1 to [tex]\(\frac{1}{5}\)[/tex]? We divide 1 by 5.
- From [tex]\(5^{-1} = \frac{1}{5}\)[/tex] to [tex]\(5^{-2} = \frac{1}{25}\)[/tex], how do we get from [tex]\(\frac{1}{5}\)[/tex] to [tex]\(\frac{1}{25}\)[/tex]? We divide [tex]\(\frac{1}{5}\)[/tex] by 5.
In all above transitions, each value is derived by dividing the previous value by 5.
Thus, the correct pattern as the exponents decrease is:
divide the previous value by 5
