Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(−3/mn^2)^−3
To simplify the expression (−3/mn^2)^−3 using the properties of exponents, we can follow these steps:
1. Start by writing the reciprocal of the expression: (−3/mn^2)^−3 = (mn^2/−3)^3.
2. Apply the property of exponents that states when raising a power to another power, you multiply the exponents: (mn^2/−3)^3 = m^3 * (n^2)^3 * (−3)^3.
3. Simplify the numerical portion of the expression: (−3)^3 = -3 * -3 * -3 = -27.
4. Rewrite the expression with only positive exponents: m^3 * (n^2)^3 * (−3)^3 = m^3 * n^(2*3) * (-27).
Finally, the simplified expression is -27m^3n^6.