$解：(2)(a×b)^n$
$=\underbrace {(a×b)×(a×b)×···×(a×b)}_{n個(gè)(a×b)相乘}$
$=a×b×a×b···×a×b$
$=\underbrace {(a×a×···×a)}_{n個(gè)a相乘}×\underbrace {(b×b×···×b)}_{n個(gè)b相乘}$
$=a^n×b^n$
$(3)①原式=(-\frac 14×4)^{1000}=1$
$②原式=(-\frac18)^2×(-\frac18)^{2022}×2×2^{2022}×4^{2022}$
$=\frac1{64}×2×(-\frac18×2×4)^{2022}$
$=\frac1{32}$
