Question

multiple-choice question simplify $3^{-4} \cdot 3^{2}$ select 2 answers $3^{2}$ $3^{-2}$ $\frac{1}{3^{2}}$ $\frac{1}{9}$ $\frac{1}{6}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.
$3^{-4} \cdot 3^{2} = 3^{-4+2} = 3^{-2}$

Step2: Convert negative exponent to positive

A negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$.
$3^{-2} = \frac{1}{3^2} = \frac{1}{9}$

Answer:

B. $3^{-2}$, D. $\frac{1}{9}$