how do i solve (27x^6)^2/3?

27x^6)^2/3

27^(2/3)*x^6(2/3)-----> this step is correct

I would change 27 to 3^3

((3^3)(^2/3 * (x^6)^2/3==> 3^6/3 * x^12/3==> 3^2x^4
the final answer is 9x^4

27^(2/3) x^(12/3)
3² x^4
9 x^4

This can be written as (27 x^6)^2/3=((27 x^6)^1/3)^2)
x^1/n means nth power of x
Therfore (27x^6)^1/3=cube root of 27x^6
=3x^2
Therefore (27x^6)^2/3=(3x^2)^2
=9x^4

(27x^6)^(2/3)
= ³√(27x^6)^2
= ³√[(27^2][x^(6 * 2)]
= ³√[27^2][x^12]
= ³√[3^2][3^2][3^2][x^4][x^4][x^4]
= 3^2x^4
= 9x^4

Your initial line is right: 27^(2/3)*x^6(2/3) but 27^2/3 is not done by multiplying it but rather it means square of the cube root of 27 or getting first cube root of 27 is 3 then squaring it gives you 9.

I think 18 x^4 is only correct.

27^(2/3)*x^6(2/3)
=cube root of 27^2 * cube root of (x^6)^2
=cube root of 729 * cube root of x^12
=9 * x^4