Let's complete the table of values by evaluating the required expressions.
We start with the given values:
- For [tex]\( x = 0 \)[/tex], we need to find the value of [tex]\( 4^{0} \)[/tex].
- For [tex]\( x = 2 \)[/tex], we need to find the value of [tex]\( 4^{-2} \)[/tex].
- For [tex]\( x = 4 \)[/tex], we need to find the value of [tex]\( 4^{-4} \)[/tex].
Given the results, we have:
[tex]\[
4^0 = 1
\][/tex]
So, [tex]\( a \)[/tex] is:
[tex]\[ a = 1 \][/tex]
Next, let's find [tex]\( 4^{-2} \)[/tex]:
[tex]\[
4^{-2} = \frac{1}{4^2} = \frac{1}{16} = 0.0625
\][/tex]
So, [tex]\( b \)[/tex] is:
[tex]\[ b = 0.0625 \][/tex]
Finally, we find [tex]\( 4^{-4} \)[/tex]:
[tex]\[
4^{-4} = 4^4 = 256
\][/tex]
So, [tex]\( c \)[/tex] is:
[tex]\[ c = 256 \][/tex]
Now we can complete the table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$4^{-x}$[/tex] \\
\hline
-1 & 4 \\
\hline
0 & 1 \\
\hline
2 & 0.0625 \\
\hline
4 & 256 \\
\hline
\end{tabular}
[tex]\[
\begin{array}{l}
a = 1 \quad b = 0.0625 \\
c = 256
\end{array}
\][/tex]
