Hi:

27^(1/3) =3. That is, the cube root of 27 is 3. This is true because 3^3=27. Now, recall the property of exponents that asserts (a^m)/(b^m)=(a/b)^m. From this property and the fact that 27^(1/3)=3, we have (1/27)^(1/3)=[1^(1/3)]/[27^(1/3)]=1/3. So, congratulations! You were correct all along.

Regards,

Rich B.