First, use this rule of exponents to simplify the #b^0# term:
#a^color(red)(0) = 1#
#(-ab^color(red)(0) * a^2b^5)^4 * 2a^3 =>#
#((-a * 1) * a^2b^5)^4 * 2a^3 =>#
#(-a * a^2b^5)^4 * 2a^3#
Next, use these rules of exponents to multiply the #a# terms within the parenthesis:
#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#(-a * a^2b^5)^4 * 2a^3 => (-a^color(red)(1) * a^color(blue)(2)b^5)^4 * 2a^3 =>#
#(-(a^color(red)(1)+color(blue)(2))b^5)^4 * 2a^3 =>#
#(-a^3b^5)^4 * 2a^3#
Then, use this rule of exponents to eliminate the exponent for the term in parenthesis:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(-a^color(red)(3)b^color(red)(5))^color(blue)(4) * 2a^3 =>#
#-a^(color(red)(3)xxcolor(blue)(4))b^(color(red)(5)xxcolor(blue)(4)) * 2a^3 =>#
#-a^12b^20 * 2a^3#
Next, rewrite the expression as:
#-2(a^12 * a^3)b^20#
Now, use this rule again to multiply the #a# terms:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#-2(a^color(red)(12) * a^color(blue)(3))b^20 =>#
#-2a^(color(red)(12)+color(blue)(3))b^20 =>#
#-2a^15b^20 =>#
