Final answer:
To simplify x^-1 * y^-2 / z^-3 with positive exponents, we can rewrite the negative exponents as fractions, then divide the fractions by multiplying the first fraction by the reciprocal of the second fraction. The simplified expression is z^3 / (x * y^2).
Step-by-step explanation:
To simplify the expression x^-1 * y^-2 / z^-3 with positive exponents, we can apply the rule that negative exponents flip the construction to the denominator or denote a division. So, x^-1 is equivalent to 1/x, y^-2 is equivalent to 1/y^2, and z^-3 is equivalent to 1/z^3. Combining these results, we get (1/x) * (1/y^2) / (1/z^3).
When we divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we multiply (1/x) * (1/y^2) by the reciprocal of (1/z^3), which is z^3.
Finally, simplifying this expression, we get z^3 / (x * y^2) as the answer.