Question

question
which expression is equivalent to \\(\frac{3^{-2}}{3^0}\\)?
answer
\\(\circ\\) \\(\frac{1}{3}\\) \\(\circ\\) 0
\\(\circ\\) 9 \\(\circ\\) \\(\frac{1}{9}\\)

Explanation:

Step1: Recall exponent rules

We know that \(a^{-n}=\frac{1}{a^{n}}\) and \(a^{0} = 1\) (\(a
eq0\)).
First, simplify the numerator \(3^{-2}\) using the negative exponent rule: \(3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}\).
Then, simplify the denominator \(3^{0}\) using the zero - exponent rule: \(3^{0}=1\).

Step2: Divide the simplified numerator by the simplified denominator

Now we have \(\frac{3^{-2}}{3^{0}}=\frac{\frac{1}{9}}{1}\).
Dividing a number by 1 gives the number itself, so \(\frac{\frac{1}{9}}{1}=\frac{1}{9}\).

Answer:

\(\frac{1}{9}\) (the option corresponding to \(\frac{1}{9}\))