First, the Excluded Values can be found by equating the denominator to #0# and then solve each variable for #0#:
#2a^2b = 0#
#a^2 = 0# therefore #a = 0#
#b = 0#
The Excluded values are #a = 0# and/or #b = 0#
To simplify the expression, rewrite the expression as:
#(3a^2b^4)/(3a^2b) + (9a^3b)/(3a^2b) - (6a^5b)/(3a^2b) =>#
#(color(purple)(cancel(color(black)(3)))color(red)(cancel(color(black)(a^2)))b^4)/(color(purple)(cancel(color(black)(3)))color(red)(cancel(color(black)(a^2)))b) + (color(purple)(cancel(color(black)(9)))3a^3color(blue)(cancel(color(black)(b))))/(color(purple)(cancel(color(black)(3)))a^2color(blue)(cancel(color(black)(b)))) - (color(purple)(cancel(color(black)(6)))2a^5color(blue)(cancel(color(black)(b))))/(color(purple)(cancel(color(black)(3)))a^2color(blue)(cancel(color(black)(b)))) =>#
#b^4/b + (3a^3)/a^2 - (2a^5)/a^2#
Next, use these rules for exponents to simplify the remaining terms:
#a = a^color(blue)(1)# and #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #a^color(red)(1) = a#
#b^color(red)(4)/b^color(blue)(1) + (3a^color(red)(3))/a^color(blue)(2) - (2a^color(red)(5))/a^color(blue)(2) =>#
#b^(color(red)(4)-color(blue)(1)) + 3a^(color(red)(3)-color(blue)(2)) - 2a^(color(red)(5)-color(blue)(2)) =>#
#b^3 + 3a^1 - 2a^3 =>#
#b^3 + 3a - 2a^3 =>#
