hw 15 exponential functions 6.1: prob\n(1 point)\nfor the function $f(x) = 4^{x+2}$, find $f(-5)$. enter…

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

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

Answer

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})