Question

hw 15 exponential functions 6.1: prob
(1 point)
for the function $f(x) = 4^{x+2}$, find $f(-5)$. enter answer as a simplified exact value.
$f(-5) = \square$ help (numbers)
preview my answers submit answers show me another
you have attempted this problem 0 times. you have 5 attempts left before new version will be
you have unlimited attempts remaining.

Explanation:

Step1: Substitute \(x = - 5\) into the function

Substitute \(x=-5\) into \(f(x)=4^{x + 2}\), we get \(f(-5)=4^{-5 + 2}\).

Step2: Simplify the exponent

Simplify \(-5 + 2=-3\), so \(f(-5)=4^{-3}\).

Step3: Use the negative - exponent rule

According to the rule \(a^{-n}=\frac{1}{a^{n}}\), when \(a = 4\) and \(n = 3\), we have \(4^{-3}=\frac{1}{4^{3}}\).

Step4: Calculate \(4^{3}\)

Since \(4^{3}=4\times4\times4 = 64\), then \(\frac{1}{4^{3}}=\frac{1}{64}\).

Answer:

\(\frac{1}{64}\)