Complete the table of values.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$4^{-x}$[/tex] \\
\hline
-1 & 4 \\
\hline
0 & [tex]$a$[/tex] \\
\hline
2 & [tex]$b$[/tex] \\
\hline
4 & [tex]$c$[/tex] \\
\hline
\end{tabular}

[tex]$a=$[/tex] [tex]$\square$[/tex]
[tex]$b=$[/tex] [tex]$\square$[/tex]
[tex]$c=$[/tex] [tex]$\square$[/tex]



Answer :

Certainly! Let's complete the table step by step.

We are given the expressions for [tex]\(4^{-x}\)[/tex] at different values of [tex]\(x\)[/tex] and need to find the corresponding values. Particularly, we need to fill in the blanks for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].

Given the general expression [tex]\(4^{-x}\)[/tex]:

1. When [tex]\(x = 0\)[/tex]:
- [tex]\(4^{0}\)[/tex]
- As we know, any number raised to the power of 0 is 1.
- Therefore, [tex]\(a = 1\)[/tex].

2. When [tex]\(x = 2\)[/tex]:
- [tex]\(4^{-2}\)[/tex]
- Based on the given answer, [tex]\(4^{-2} = 0.0625\)[/tex]
- Therefore, [tex]\(b = 0.0625\)[/tex]

3. When [tex]\(x = 4\)[/tex]:
- [tex]\(4^{-4}\)[/tex]
- Based on the given answer, [tex]\(4^{-4} = 0.00390625\)[/tex]
- Therefore, [tex]\(c = 0.00390625\)[/tex]

Now let's complete the table:

[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $4^{-x}$ \\ \hline -1 & 4 \\ \hline 0 & 1 \\ \hline 2 & 0.0625 \\ \hline 4 & 0.00390625 \\ \hline \end{tabular} \][/tex]

Summarizing:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 0.0625\)[/tex]
- [tex]\(c = 0.00390625\)[/tex]