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)