What is the simplified form of the following? $$2x^2 \cdot 3x^3$$

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One way to visualize what is going on is to write out each individual term.

$$2x^2 \cdot 3x^3$$ $$2 \cdot x \cdot x \cdot 3 \cdot x \cdot x \cdot x$$ $$\underbrace{2 \cdot 3}_\text{constants}\cdot \underbrace{ x \cdot x \cdot x \cdot x \cdot x}_\text{variables}$$ $$= \boxed{6x^5}$$

Given exponential terms with the same base, we can multiply by adding the exponents:

$$x^a \cdot x^b = x^{a+b}$$

Accordingly,

$$2x^2 \cdot 3x^3$$ $$2 \cdot 3 \cdot x^2 \cdot x^3$$ $$=6x^{2+3}$$ $$=\boxed{6x^5}$$