9th root of 9x squared can be written as

#color(white)("XXX")(9x)^(2/9)=(3^2)^(2/9) * x^(2/9)#

#color(white)("XXXXXX")=3^(4/9) * x^(2/9)#

6th root of 27x raised to 5 can be written as

#color(white)("XXX")(27x)^(5/6)=(3^3)^(5/6) * x^(5/6)#

#color(white)("XXXXXXX")=3^(15/6) * x^(5/6)#

#color(white)("XXXXXXX")=3^(5/2) * x^(5/6)#

#(9x)^(2/9) xx (27x)^(5/6)#

#color(white)("XXX")=3^(4/9) * x^(2/9) xx 3^(5/2) * x^(5/6)#

#color(white)("XXX")=3^(4/9) * 3^(5/2) xx x^(2/9) * x^(5/6)#

#color(white)("XXX")=3^(10/9) * x^(5/27)#

#color(white)("XXX")=3^(30/27) * x^(5/27)#

#color(white)("XXX")=(3^6)^(5/27) * x ^(5/27)#

#color(white)("XXX")=729^ (5/27) * x^(5/27)#

#color(white)("XXX")=(729x)^(5/27)#