First, we can use this rule for exponents to start the simplification process:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(a^color(red)(-1)b^color(red)(1/3)*a^color(red)(-4/3)b^color(red)(2))^color(blue)(2) ->#
#(a^(color(red)(-1)xx color(blue)(2))b^(color(red)(1/3)xxcolor(blue)(2))*a^(color(red)(-4/3)xxcolor(blue)(2))b^(color(red)(2)xxcolor(blue)(2))) ->#
#a^-2b^(2/3)*a^(-8/3)b^4#
Next, we can group like terms:
#(a^-2*a^(-8/3))(b^(2/3)*b^4)#
Next, we can use this rule of exponents to further simplify:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))#
#(a^color(red)(-2)*a^color(blue)(-8/3))(b^color(red)(2/3)*b^color(blue)(4))#
#(a^color(red)(-2xx3/3)*a^color(blue)(-8/3))(b^color(red)(2/3)*b^color(blue)(4xx3/3))#
#(a^color(red)(-6/3)*a^color(blue)(-8/3))(b^color(red)(2/3)*b^color(blue)(12/3))#
#(a^(color(red)(-6/3)+color(blue)(-8/3)))(b^(color(red)(2/3)+color(blue)(12/3)))#
#a^(-14/3)b^(14/3)#
We can now use this rule of exponents to further transform this expression:
#x^color(red)(a) = 1/x^color(red)(-a)#
#b^(14/3)/a^(- -14/3)#
#b^(14/3)/a^(14/3)#
or
#(b/a)^(14/3)#
