Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$.
$f\left(x\right)={\left(\frac{1}{2}\right)}^x$

• A. Exponential function, $f\(\left\)(4\(\right\))=\(\frac{1}{16}\)$
• B. Exponential function, $f\(\left\)(4\(\right\))=-16$
• C. Not an exponential function
• D. Exponential function, $f\left(4\right)=2$

Answer: (A)

Verified step by step guidance

1. Identify the exponential function you need to evaluate. An exponential function generally has the form \(f(x) = a^{x}\), where \(a\) is the base and \(x\) is the exponent.
2. Substitute the given value of \(x\) into the function. This means replacing every occurrence of \(x\) in the expression with the specific number provided.
3. Apply the exponentiation rule by raising the base \(a\) to the power of the substituted exponent. Remember that \(a^{x}\) means multiplying \(a\) by itself \(x\) times if \(x\) is a positive integer.
4. If the exponent is negative or a fraction, recall the rules: \(a^{-x} = \frac{1}{a^{x}}\) and \(a^{\frac{m}{n}} = \sqrt[n]{a^{m}}\). Use these to simplify the expression accordingly.
5. Simplify the resulting expression step-by-step to find the value of the exponential function at the given input.