Find the exponential function f(x)=a^x whose graph goes through the point (2,(1)/(16)) a=square

To find the value of $a$ in the exponential function $f(x) = a^x$ that passes through the point $(2, \frac{1}{16})$, we can substitute the coordinates of the point into the function and solve for $a$.

Given:
$$f(2) = \frac{1}{16}$$

Substitute $x = 2$ into the function:
$$a^2 = \frac{1}{16}$$

To solve for $a$, take the square root of both sides:
$$a = \pm \sqrt{\frac{1}{16}}$$

Simplify the square root:
$$a = \pm \frac{1}{4}$$

Since the base of an exponential function is typically positive, we take the positive value:
$$a = \frac{1}{4}$$

Therefore, the value of $a$ is:
$$a = \frac{1}{4}$$