$解：①8²⁰²²×(-0.125)²⁰²²\ $
$=8²⁰²²×0.125²⁰²²$
$=(8×0.125)²⁰²²\ $
$=1²⁰²²$
$=1.\ $
$②(\frac{12}{5})¹¹×(\frac{5}{6})¹³×(\frac{1}{2})¹²$
$=(\frac{12}{5})¹¹×(\frac{5}{6})¹¹×(\frac{5}{6})²×(\frac{1}{2})¹¹×\frac{1}{2}\ $
$=(\frac{12}{5}×\frac{5}{6}×\frac{1}{2})¹¹×\frac{25}{36}×\frac{1}{2}\ $
$=1¹¹×\frac{25}{72}$
$=1×\frac{25}{72}$
$=\frac{25}{72}.$
