170 Given a positive integer $n$ and a constant $a>0, x$ is any positive number, then the minimum value of $\frac{\left(a^{n}+x^{n}\right) \cdot(a+x)^{n}}{x^{n}}$ is
$170 \quad 2^{n+1} \cdot a^{n}$.
$$
\frac{\left(a^{n}+x^{n}\right) \cdot(a+x)^{n}}{x^{n}} \geqslant \frac{2 \cdot \sqrt{a^{n} \cdot x^{n}} \cdot(2 \cdot \sqrt{a \cdot x})^{n}}{x^{n}}=2^{n+1} \cdot a^{n},
$$

The equality holds if and only if $x=a$, so the minimum value is $2^{n+1} \cdot a^{n}$.