3a^-2b×24b^-1a^-1÷9a^-4b^-3,
(3b/a²)(24/(ab))÷(9/(a⁴b³)),
(3b/a²)(24/(ab))(a⁴b³/9),
(b/a²)(8/(ab))(a⁴b³) because 3×24/9=8,
(8/a³)(a⁴b³),
8ab³.
Another way is to take each variable in turn:
a^(-2-1+4)=a^1=a;
b^(1-1+3)=b^3=b³;
Then the numbers: 3×24÷9=8.
Combine: 8ab³.
