3. If non-zero real numbers $a, b, c$ are the $m$-th, $n$-th, $p$-th terms of an arithmetic sequence, and also the $m$-th, $n$-th, $p$-th terms of a geometric sequence, then the value of $a^{b-c} b^{c-a} c^{a-b}$ is $\qquad$ .
Let the arithmetic sequence be $a_{k}=A+k d$, and the geometric sequence be $b_{k}=B q^{k}$, then $a=A+m d=B q^{m}$,
$$
\begin{array}{l}
b=A+n d=B q^{n}, c=A+p d=B q^{p} \Rightarrow b-c=(n-p) d, c-a=(p-m) d, \\
a-b=(m-n) d \Rightarrow a^{b-c} b^{c-a} c^{a-b}=B^{(n-p) d+(p-m) d+(m-n) d} \cdot q^{m(n-p) d+n(p-m) d+p(m-n) d}
\end{array}
$$
$=B^{0} \cdot q^{0}=1$, so the value of $a^{b-c} b^{c-a} c^{a-b}$ is 1.