1. The problem is to calculate the value of $(-50)^3$. 2. The formula for raising a number to a power is $a^n = a \times a \times \cdots \times a$ (n times). 3. Here, $a = -50$ and $n = 3$, so we multiply $-50$ by itself three times: $$(-50)^3 = (-50) \times (-50) \times (-50)$$ 4. First, multiply the first two terms: $$(-50) \times (-50) = 2500$$ 5. Now multiply the result by the last term: $$2500 \times (-50) = -125000$$ 6. Therefore, the final answer is: $$\boxed{-125000}$$ This is because multiplying two negative numbers gives a positive, but multiplying a positive by a negative gives a negative.