hard algebra

Let x =  sqrt 9 sqrt27 sqrt128.......

square it      square it     square it again

and you have     x⁸ =    612220032 sqrt 9 sqrt27sqrt128.....    the red part is 'x'   

(61222032 is 9⁴27²128)

                           x⁸  =61222032 x

                           x^7 = 612220032

                            x = 18                          ????

Find the Prime Factors of each:

1 - 9 = 3^2   and   27 =3^3    and    128  =2^7

2 - By taking an infinite number of Square Roots, The exponents will eventually converge to 1 for each Prime Factor.

3 - Then, will be left with the factors themselves multiplied by each other.

4 - Therefore: 3  x  3  x  2 = 18