Question

evaluate the expression \\(\frac{3^2}{3^4}\\). rewrite the expression using a positive power of 3. \\(\frac{3^2}{3^4} = 3^{-2} =?\\) options: \\(\frac{1}{3^{-2}}\\), \\(\frac{1}{3^2}\\), \\(-\frac{1}{3^2}\\), \\(-\frac{1}{3^{-2}}\\)

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \( a^{-n} = \frac{1}{a^{n}} \) for any non - zero number \( a \) and positive integer \( n \).

Step2: Apply the rule to \( 3^{-2} \)

We have \( a = 3 \) and \( n=2 \). Using the rule \( a^{-n}=\frac{1}{a^{n}} \), when \( a = 3 \) and \( n = 2 \), we get \( 3^{-2}=\frac{1}{3^{2}} \).

Answer:

\(\frac{1}{3^{2}}\) (or we can also simplify \( \frac{1}{3^{2}}=\frac{1}{9} \), but since the question asks to rewrite using a positive power of 3, \(\frac{1}{3^{2}}\) is the form with a positive power of 3)