(-a^2b/b^2c) divided by (a^2c/B^2c^2)?

Dividing fractions is the same as muyltiplying by the reciprocal, so:

(-a²b / b²c) / (a²c / b²c²)
(-a²b / b²c) * (b²c² / a²c)

Now multiply the fractions:

-a²b³c² / a²b²c²

Now simply:

-b

(-a^2b/b^2c)/(a^2c/b^2c^2)
= (-a^2/bc)/(a^2/b^2c)
= [-a^2/bc][1/(a^2/b^2c)]
= [-a^2/bc][1(b^2c/a^2)]
= [-a^2/bc][b^2c/a^2]
= -a^2b^2c/a^2bc
= (-a^2/a^2)(b^2/b)(c/c)
= -1(b)(1)
= -b