1. The problem is to simplify $3^4 \times 3^2$ into a single expression using indices. 2. The rule for multiplying powers with the same base is: $$a^m \times a^n = a^{m+n}$$ where $a$ is the base and $m,n$ are the exponents. 3. Applying this rule to $3^4 \times 3^2$, we add the exponents: $$3^{4+2}$$ 4. Simplifying the exponent sum: $$3^6$$ 5. Therefore, the simplified form of $3^4 \times 3^2$ is $3^6$.