Expressing the given expression as a power of a rational number with a positive exponent involves simplifying and rearranging the terms using the rules of exponents.

1. Simplify the exponents:
- The exponent of 3 is -6.
- The exponent of 9 is 2.
- The exponent of 27 is -1.

2. Apply the rule of negative exponents:
- To simplify the expression, we can use the rule that states a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
- Rewrite 3^-6 as 1/3^6.
- Rewrite 27^-1 as 1/27^1.

3. Rearrange the terms:
- Rewrite the expression as (1/3^6) / (9^2) * (1/27^1).

4. Simplify the expression:
- Simplify the exponents: 3^6 = 729, 9^2 = 81, and 27^1 = 27.
- Substitute the values and simplify the expression further: (1/729) / 81 * (1/27).
- Simplify the division: (1/729) / 81 = 1/59241.
- Simplify the multiplication: (1/59241) * (1/27).
- Multiply the numerators: 1 * 1 = 1.
- Multiply the denominators: 59241 * 27 = 1603807.
- The simplified expression is 1/1603807.

5. Express as a power of a rational number with a positive exponent:
- Rewrite the expression as 1/(3^6 * 9^2 * 27^1).
- Express each base as a power of a rational number with a positive exponent: 3^6 = (3^2)^3 = (9)^3, 9^2 = (3^2)^2 = (9)^2, and 27^1 = (3^3)^1 = (27)^1.
- Substitute the values: 1/((9)^3 * (9)^2 * (27)^1).
- Combine the bases with the same exponent: 1/(9^(3 + 2 + 1)).
- Simplify the exponent: 1/9^6.

Therefore, the given expression, 3^-6 / 9^2 * 27^-1, can be expressed as a power of a rational number with a positive exponent as 1/9^6.