Answer
False
Work Step by Step
RECALL:
$a^m \cdot a^n = a^{m+n}$
The rule above states that when multiplying factors with the same base, add the exponents and retain the base.
Thus,
$2x^2 \cdot 3x^3 = 6x^{2+3}=6x^5$
Thus, the given statement is false.