Answer:
[tex]f(5)=1024[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=a^x[/tex]
Where a>0.
We know that f(4)=256. Therefore:
[tex]\displaystyle f(4)=a^4=256[/tex]
So:
[tex]a^4=256[/tex]
Find the value of a. Take the fourth root of both sides:
[tex]a=\sqrt[4]{256}=4[/tex]
Therefore, our function is:
[tex]f(x)=4^x[/tex]
Hence:
[tex]f(5)=4^5=1024[/tex]
