First, we can rewrite the term with the exponent:
#(a^2b(b - 3))/(b^3color(red)((b - 3)^2)) ->#
#(a^2b(b - 3))/(b^3color(red)((b - 3))color(red)((b - 3))) ->#
We can now cancel one of the common terms:
#(a^2bcolor(red)(cancel(color(black)((b - 3)))))/(b^3color(red)((b - 3))cancel(color(red)((b - 3)))) ->#
#(a^2b)/(b^3(b - 3))#
We can now simplify the #b# terms with two exponent rules.
Rule: #color(red)(x^a)/color(blue)(x^b) = color(red)(1)/color(blue)(x^(b-color(red)(a)))#
Rule: #color(red)(x = x^1)#
#(a^2color(red)(b))/(color(blue)(b^3)(b - 3)) ->#
#(a^2color(red)(b^1))/(color(blue)(b^3)(b - 3)) ->#
#a^2/(color(blue)(b^(3-color(red)(1))color(black)((b - 3))) ->#
#a^2/(b^2(b - 3))#
Now we can expand the terms in the denominator using another rule of exponents:
Rule: #color(red)(x^a) * color(blue)(x^b) = x^(color(red)(a) + color(blue)(b)#
#a^2/(color(red)(b^2)(color(blue)(b) - 3))#
#a^2/(color(red)(b^2)(color(blue)(b^1) - 3))#
#a^2/(b^(color(red)(2) + color(blue)(1)) - 3b^2)#
#a^2/(b^3 - 3b^2)#
