To evaluate $abc^2$ given $a = -3$, $b = 6$, and $c = -8$, we substitute these values into the expression:

$abc^2 = (-3)(6)((-8)^2)$

Step 1: Evaluate $c^2$

$(-8)^2 = 64$

Step 2: Multiply the results

$abc^2 = (-3)(6)(64)$

Step 3: Calculate step-by-step

• $(-3)(6) = -18$
• $(-18)(64) = -1152$

Final Answer:

$abc^2 = -1152$

Let me know if you want further clarification or details.

Here are some related questions to deepen your understanding:

1. What happens if one of the variables is zero in the expression $abc^2$?
2. How does the exponent affect the result when the base is negative, such as $(-8)^2$?
3. What is the difference between evaluating $abc^2$ and $a^2b^2c^2$?
4. How would the result change if $c$ were a positive value?
5. Can you write $abc^2$ in terms of powers and solve it for any general values of $a, b, c$?

Tip: Always simplify exponents first before handling the multiplications to avoid errors.