To simplify this expression, we can use the rule of exponents that states when dividing two numbers with the same base, we subtract the exponents.

So, (-1/3)⁹ : (-1/3)⁵ = (-1/3)^(9-5) = (-1/3)⁴.

To simplify further, we can multiply the numerator and denominator by (-1/3)²:

(-1/3)⁴ = (-1/3)⁶ / (-1/3)² = (1/729) / (1/9).

To divide by a fraction, we can multiply by its reciprocal:

(1/729) / (1/9) = (1/729) * (9/1) = 9/729.

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

9/729 = 1/81.

Therefore, (-1/3)⁹ : (-1/3)⁵ = 1/81.