Suppose $81^x = 64$. what is $27^{x+1}$?

(3^4)^x = 4^3

3^(4x) = 4^3

3^x = 4^(3/4)

(3^x) ^3 = (4^(3/4))^3
3^(3x) = 4^(3*3/4)
(3^3)^x = 4^(9/4) = (2^2)^(9/4) = 2^(2*9/4) = 2^(9/2)

27^x = 2^(9/2) = 2^(8/2) * 2^(1/2) = 2^4 * 2^(1/2)

27^x = 16 sqrt(2)

27^x * 27 = 16*27 sqrt(2)

27^(x + 1) = 432 sqrt(2)