Question

multiple-choice question simplify $3^{-6} \cdot 3^{4}$ into one exponent (with a negative exponent). $3^{2}$ $3^{-2}$ $3^{-24}$

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$.
For $3^{-6} \cdot 3^4$, we calculate the sum of exponents: $-6 + 4 = -2$.
So the expression simplifies to $3^{-2}$.

Step2: Verify negative exponent requirement

The result has a negative exponent, which matches the problem's requirement.

Answer:

$3^{-2}$ (the second option)