Question

use the function below to find $f(-2)$.
$f(x) = 5^x$
a. $\frac{1}{25}$
b. $-10$
c. $-25$
d. $\frac{1}{10}$

Explanation:

Step1: Substitute \( x = -2 \) into \( f(x) \)

We have the function \( f(x) = 5^x \). To find \( f(-2) \), we substitute \( x = -2 \) into the function, so we get \( f(-2)=5^{-2} \).

Step2: Apply the negative exponent rule

The negative exponent rule states that \( a^{-n}=\frac{1}{a^n} \) (where \( a
eq0 \) and \( n \) is a positive integer). Using this rule, \( 5^{-2}=\frac{1}{5^2} \).

Step3: Calculate \( 5^2 \)

We know that \( 5^2 = 5\times5 = 25 \). So, \( \frac{1}{5^2}=\frac{1}{25} \).

Answer:

A. \(\frac{1}{25}\)