How can I simplify the expression 3/x² divided by 1/x³?

To simplify the expression 3/x² divided by 1/x³, we first need to understand the mathematical operation involved:

The expression can be rewritten using division:

3/x² ÷ 1/x³

Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division as multiplication:

3/x² × x³/1

Now, we multiply the numerators and the denominators:

(3 × x³) / (x² × 1)

This simplifies to:

3x³ / x²

Next, we can further simplify x³ / x². According to the laws of exponents, when you divide two powers with the same base, you subtract the exponents:

x³ / x² = x^3-2 = x¹ = x

Substituting this back into our expression gives:

3x / 1

And simplifying it further, we find:

3x

Thus, the simplified form of the expression (3/x²) ÷ (1/x³) is 3x.