Final answer:
To simplify the expression ((3m^(-2)n)^(-3))/(6mn^(-2)), you can start by applying the negative exponent rule and rewriting the expression. Then, you can cancel out common terms in the numerator and denominator. Finally, you can rewrite the expression in simplified form.
Step-by-step explanation:
To simplify the expression ((3m^(-2)n)^(-3))/(6mn^(-2)), we can start by applying the negative exponent rule. A negative exponent can be rewritten as the reciprocal of the positive exponent. So, the expression becomes (6mn^2)/((3m^2n)^3). Next, we can simplify the cube of the expression in the denominator by expanding it: (3m^2n)^3 = (3m^2)^3 * n^3 = 27m^6 * n^3. Now, we can cancel out common terms in the numerator and denominator. Cancelling out mn^2 and 27m^6, we are left with (1/3) * m^(-4) * n^(-1). To put this in a simplified form, we can use the negative exponent rule again, obtaining (1/3) * (1/m^4) * (1/n).
Now, when we multiply fractions, we multiply the numerators and the denominators separately. So, (1/3) * (1/m^4) * (1/n) = 1/(3m^4n). Finally, we can rewrite this expression as (1/3m^4n).