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]
