Solve for x: x to the negative 3rd power is equal to 27 over 64

Remember what a negative exponent means ... it's just a positive exponent
in the denominator of a fraction. 'x' to negative 3rd power is the same as 1/x³ .

1/x³ = 27/64

Take the reciprocal of each side:

x³ = 64/27

x= ∛64/27 = ∛64 / ∛27.

64 is the perfect cube of 4.
27 is the perfect cube of 3.

x = 4/3 .