The expression $\left(-\frac{4}{3}\right)^2$ simplifies as follows:

1. Square the numerator and denominator separately: $\left(-\frac{4}{3}\right)^2 = \frac{(-4)^2}{3^2} = \frac{16}{9}$

So, $\left(-\frac{4}{3}\right)^2 = \frac{16}{9}$.

Would you like further details on the steps?

Here are some related questions to explore:

1. What happens if the exponent were odd, such as $(-4/3)^3$?
2. How would this expression change with a negative exponent?
3. How do we simplify square roots of fractions?
4. How would we solve $(a/b)^n$ in general?
5. How does squaring affect positive and negative numbers?

Tip: Remember, squaring any real number—positive or negative—results in a positive value.