Calculate -3³ vs (-3)³: Understanding Negative Number Exponents

To solve this problem, we'll follow these steps:

• Step 1: Calculate $-3^3$ and $(-3)^3$.
• Step 2: Add the results from both calculations.

Now, let's break this down further:
Step 1: First, compute $-3^3$.
The expression $-3^3$ should be interpreted as $- (3^3)$. This means we first calculate $3^3$, which is $3 \times 3 \times 3 = 27$. The negative sign in front gives us $-27$.
Next, calculate $(-3)^3$.
Here, the base is $-3$, so we calculate $(-3) \times (-3) \times (-3)$. This gives us:
- Multiply the first two factors: $(-3) \times (-3) = 9$.
- Multiply the result by the last factor: $9 \times (-3) = -27$.
So, $(-3)^3 = -27$.

Step 2: Add the results $-27 + (-27)$.
This computation is $-27 - 27 = -54$.

Therefore, the solution to the problem is $-54$.