First, let's rewrite the division as a multiplication by the reciprocal:
$$
\frac{(x-p)^{n}}{x^{-2}} \cdot \frac{x^{-6}}{(x-p)^{2n}}
$$
Now, let's use the properties of exponents to simplify the expression:
$$
\frac{(x-p)^{n}(x^{-6})}{x^{-2}(x-p)^{2n}} =
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