Compare Cube Values: 3³ vs (-3)³ Mathematical Analysis

To compare $3^3$ and $-(-3)^3$, we will calculate each expression separately and then determine their relationship:

• Calculate $3^3$:

  $3^3$ means $3 \times 3 \times 3$.

  First, $3 \times 3 = 9$.

  Then, $9 \times 3 = 27$.

  Therefore, $3^3 = 27$.

• Calculate $-(-3)^3$:

  $(-3)^3$ means $(-3) \times (-3) \times (-3)$.

  First, $(-3) \times (-3) = 9$. (two negatives multiply to a positive)

  Then, $9 \times (-3) = -27$. (positive times negative is negative)

  Thus, $(-3)^3 = -27$.

  Considering the negative sign: $-(-3)^3 = -(-27) = 27$.

After calculating, we find that both expressions equal 27. Thus, they are equal.

The correct choice is:

$=$