To simplify the expression (3⁻¹ x 6⁻¹) / 3³, we can follow the order of operations (PEMDAS/BODMAS) and simplify the exponents first:
3⁻¹ means the reciprocal of 3, which is 1/3.
6⁻¹ means the reciprocal of 6, which is 1/6.
3³ means 3 raised to the power of 3, which is 27.
Now we can substitute these values into the expression:
(1/3 x 1/6) / 27
Next, we can simplify the multiplication in the numerator:
1/18 / 27
To divide fractions, we can multiply the numerator by the reciprocal of the denominator:
1/18 x 1/27
Multiplying the numerators and the denominators together:
1 x 1 / 18 x 27
This simplifies to:
1/486
Therefore, (3⁻¹ x 6⁻¹) / 3³ simplifies to 1/486.