Sure, let's calculate the values step-by-step for the function [tex]\( f(x) = 4^x \)[/tex].
1. Calculate [tex]\( f(5) \)[/tex]:
[tex]\[
f(5) = 4^5
\][/tex]
2. Calculate [tex]\( 4^5 \)[/tex]:
[tex]\[
4^5 = 4 \times 4 \times 4 \times 4 \times 4
\][/tex]
By multiplying the numbers, we get:
[tex]\[
4 \times 4 = 16 \quad \text{(first pair)}
\][/tex]
[tex]\[
16 \times 4 = 64 \quad \text{(second pair)}
\][/tex]
[tex]\[
64 \times 4 = 256 \quad \text{(third pair)}
\][/tex]
[tex]\[
256 \times 4 = 1024 \quad \text{(fourth pair)}
\][/tex]
Therefore:
[tex]\[
f(5) = 1024
\][/tex]
3. Calculate [tex]\( f(6) \)[/tex]:
[tex]\[
f(6) = 4^6
\][/tex]
4. Calculate [tex]\( 4^6 \)[/tex]:
[tex]\[
4^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4
\][/tex]
By multiplying the numbers, we get:
[tex]\[
4 \times 4 = 16 \quad \text{(first pair)}
\][/tex]
[tex]\[
16 \times 4 = 64 \quad \text{(second pair)}
\][/tex]
[tex]\[
64 \times 4 = 256 \quad \text{(third pair, as before)}
\][/tex]
[tex]\[
256 \times 4 = 1024 \quad \text{(fourth pair, as before)}
\][/tex]
[tex]\[
1024 \times 4 = 4096 \quad \text{(fifth pair)}
\][/tex]
Therefore:
[tex]\[
f(6) = 4096
\][/tex]
To summarize the results:
[tex]\[
f(5) = 1024
\][/tex]
[tex]\[
f(6) = 4096
\][/tex]
