Answer
$f(x)=\frac{1}{4}^x$
Work Step by Step
First, we have to find the function, by calculating the value of the base, $a$.
If the function contains this point (-3,64), then $f(-3)=64$,
This means: $a^{-3}=64$.
By the law of exponents: $a^{-x}=(\frac{1}{a})^x$
Thus, the equation above is equivalent to:
$(\frac{1}{a})^{3}=64$
We take the cube root of both sides:
$\frac{1}{a}=4
\\a \cdot \frac{1}{a} = 4 \cdot a
\\1=4a
\\\frac{1}{4}=a$
Therefore, with $a=\frac{1}{4}$, the function is:
$f(x)=(\frac{1}{4})^x$.