What is the simplified form of (1 / x²) ÷ (3 / x³)?

To simplify the expression (1 / x²) ÷ (3 / x³), we can start by rewriting the division as multiplication by the reciprocal. This can be expressed as:

1 / x² * x³ / 3

Now, we can combine the fractions:

1 * x³ / (3 * x²) = x³ / (3x²)

Next, we can simplify the fraction further. We can cancel x² in the numerator and denominator:

x³ / (3x²) = x^3-2 / 3 = x¹ / 3 = x / 3

Thus, the simplified form of the original expression is:

x / 3