To evaluate the multi-variable expression $3ab^2$ when a=-rac{2}{3} and b=-rac{1}{2}, carefully substitute the fractional values and follow the order of operations:

1. Substitute: Insert the fractions into the expression using parentheses for clarity: 3\left(-rac{2}{3} ight)\left(-rac{1}{2} ight)^2.
2. Simplify exponents: Square the negative fraction. Remember that a negative number squared becomes positive: \left(-rac{1}{2} ight)^2 = rac{1}{4}. The expression is now 3\left(-rac{2}{3} ight)\left(rac{1}{4} ight).
3. Multiply fractions: Multiply the parts to form a single fraction: rac{3 \cdot (-2) \cdot 1}{1 \cdot 3 \cdot 4}.
4. Divide out common factors: Cancel the common factor of $3$ and then simplify rac{-2}{4} by dividing out $2$. The final value is -rac{1}{2}.