First, convert this from it's radical form to an exponent form using this rule for exponents:
#root(color(red)(n))(x) = x^(1/color(red)(n))#
#root(color(red)(3))(27x^15y^24) = (27x^15y^24)^(1/color(red)(3))#
Next, rewrite #27# as #3 xx 3 xx 3 = 3^3#
#(27x^15y^24)^(1/color(red)(3)) = (3^3x^15y^24)^(1/3)#
Now, use these rules for exponents to complete the simplification:
#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))# and #a^color(red)(1) = a#
#(3^color(red)(3)x^color(red)(15)y^color(red)(24))^color(blue)(1/3) = 3^(color(red)(3) xx color(blue)(1/3))x^(color(red)(15) xx color(blue)(1/3))y^(color(red)(24) xx color(blue)(1/3)) = 3^(3/3)x^(15/3)y^(24/3) =#
#3^color(red)(1)x^5y^8 = 3x^5y^8#
