divide 9√33 / 27√11

To divide these two expressions, we can multiply the numerator and denominator of the first expression by the conjugate of the denominator of the second expression, and then simplify.

The conjugate of 27√11 is -27√11, so our expression becomes:

(9√33 / 27√11) * (-27√11 / -27√11)

Now let's simplify this expression:

(9 * -27 * √33 * √11) / (27 * -27 * √11 * √11)

-243 * √(33 * 11) / -729 * 11

-243√363 / -7992

Since the numerator and denominator have a common factor of -9, we can simplify further:

27√363 / 888