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)
