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 \( a \).<br /><br />Given:<br />\[ f(2) = \frac{1}{16} \]<br /><br />Substitute \( x = 2 \) into the function:<br />\[ a^2 = \frac{1}{16} \]<br /><br />To solve for \( a \), take the square root of both sides:<br />\[ a = \pm \sqrt{\frac{1}{16}} \]<br /><br />Simplify the square root:<br />\[ a = \pm \frac{1}{4} \]<br /><br />Since the base of an exponential function is typically positive, we take the positive value:<br />\[ a = \frac{1}{4} \]<br /><br />Therefore, the value of \( a \) is:<br />\[ a = \frac{1}{4} \]