(1/64)^x = 1/512 what is x?

1/64 = 1/2^6    1/512 = 1/2^9   ..so we have..

(1/2^6)^x  = (1/2)^9 =

(1/2)^(6x) = (1/2)^9      we have like bases, so equating exponents, we have

6x =9   divide by 6

x = 9/6 = 3/2

$$\\(1/64)^x = 1/512 \\ $turn both sides upside down and you get $ 64^x=512\\\\ $method 1$\\ 64^x=512\\ log64^x=log512\\ xlog64=log512\\ x=\frac{log512}{log64}\\ x=1.5\\\\ $method2$\\ 64^x=512\\ 64=2^6\quad and \quad 512=2^8\\ (2^6)^x=2^9\\ 2^{6x}=2^9\\ 6x=9\\ x=9/6=1.5$$