Question

simplify.
\\(\frac{3^2}{3^4}\\) =?
options: (3^{-2}), (3^2), (3^6), (3^8)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^m}{a^n} = a^{m - n} \), where \( a = 3 \), \( m = 2 \), and \( n = 4 \).
\[
\frac{3^2}{3^4}=3^{2 - 4}
\]

Step2: Calculate the exponent

Simplify the exponent \( 2 - 4 \):
\[
3^{2 - 4}=3^{-2}
\]

Answer:

\( 3^{-2} \) (corresponding to the option with \( 3^{-2} \))