which expression is equivalent to $(3^{2})^{-2}$?\n-81\n-12\n$\frac{1}{81}$\n$\frac{1}{12}$
which expression is equivalent to $(3^{2})^{-2}$?\n-81\n-12\n$\frac{1}{81}$\n$\frac{1}{12}$
Answer
Explanation:
Step1: Calculate the inner - exponent
First, calculate $3^{2}=9$.
Step2: Apply the negative - exponent rule
We have $(3^{2})^{-2}=9^{-2}$. According to the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$, when $a = 9$ and $n = 2$, $9^{-2}=\frac{1}{9^{2}}$.
Step3: Calculate the final result
Since $9^{2}=81$, then $\frac{1}{9^{2}}=\frac{1}{81}$.
Answer:
$\frac{1}{81}$