Answer:
[tex]f(x)=6(\frac{1}{16})^x[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=6(\frac{1}{4})^{2x}[/tex]
The exponent property:
[tex](x)^{ab}=(x^a)^b[/tex]
Using this property, we can rewrite this function as
[tex]f(x)=6((\frac{1}{4})^2)^{x}[/tex]
Now, we can further simplify this expression as
[tex]f(x)=6(\frac{1}{4^2})^{x}\\\\f(x)=6(\frac{1}{16})^x[/tex]
Hence, third option is correct.
