Question

evaluate the expression \\(\frac{3^2}{3^4}\\). simplify. \\(\frac{3^2}{3^4} = \\)? with 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} $. Here, $ a = 3 $, $ m = 2 $, and $ n = 4 $.
$$ \frac{3^2}{3^4} = 3^{2 - 4} $$

Step2: Simplify the exponent

Calculate $ 2 - 4 = -2 $. So, $ 3^{2 - 4} = 3^{-2} $.

Answer:

$3^{-2}$ (corresponding to the option: $3^{-2}$)