\begin{tabular}{|c|c|}
\hline
Powers of 5 & Value \\
\hline
[tex]$5^3$[/tex] & 125 \\
\hline
[tex]$5^2$[/tex] & 25 \\
\hline
[tex]$5^1$[/tex] & 5 \\
\hline
[tex]$5^0$[/tex] & 1 \\
\hline
[tex]$5^{-1}$[/tex] & [tex]$\frac{1}{5}$[/tex] \\
\hline
[tex]$5^{-2}$[/tex] & [tex]$\frac{1}{25}$[/tex] \\
\hline
\end{tabular}

What is the pattern as the exponents decrease?

A. Subtract 5 from the previous value

B. Subtract 100 from the previous value

C. Divide the previous value by 5

D. Divide the previous value by 25



Answer :

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