Simplify the expression $p^2 \cdot 3p^{-3}$.

1. Problem Description

Simplify the expression $p^2 \cdot 3p^{-3}$.

2. Solution Steps

First, we can rewrite the expression by grouping the constant term and the $p$ terms together:

$p^2 \cdot 3p^{-3} = 3 \cdot p^2 \cdot p^{-3}$

Next, we can use the property of exponents that states when multiplying terms with the same base, we add the exponents: $a^m \cdot a^n = a^{m+n}$. In this case, $a=p$, $m=2$, and $n=-3$. Therefore:

$p^2 \cdot p^{-3} = p^{2+(-3)} = p^{-1}$

Substituting this back into the expression, we have:

$3 \cdot p^2 \cdot p^{-3} = 3 \cdot p^{-1}$

Finally, we can rewrite $p^{-1}$ as $\frac{1}{p}$:

$3p^{-1} = 3 \cdot \frac{1}{p} = \frac{3}{p}$

3. Final Answer

The simplified expression is $\frac{3}{p}$.