Compare Expressions: -2⁴ vs -(-2)⁴ - Which is Greater?

Let's address the problem by evaluating each expression separately:

Step 1: Evaluate $-2^4$.
Here, the expression represents the negative of $2^4$. The correct interpretation is $-(2^4)$.
Calculate $2^4 = 2 \times 2 \times 2 \times 2 = 16$.
Thus, $-2^4 = -16$.

Step 2: Evaluate $-(-2)^4$.
In this expression, $(-2)$ is raised to the power 4 first. Because 4 is an even number, $(-2)^4$ results in a positive value, specifically:
$(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16$.
Therefore, $-(-2)^4 = -16$.

Step 3: Compare the results.
We now compare the two outcomes:

• $-2^4 = -16$
• $-(-2)^4 = -16$

Both expressions evaluate to $-16$, hence they are equal.

Conclusion: $-2^4$ and $-(-2)^4$ are equal. Therefore, the relationship is $=$.