Question

All of the following are equivalent except _____.

(-2)^4
-2^4
(-2)(-2)(-2)(-2)
2^4

Answer 1

To analyze the expressions, we will calculate each of them:

1. \( (-2)^4 \):
\[
(-2) \times (-2) \times (-2) \times (-2) = 16.
\]

2. \( -2^4 \):
This is interpreted as \( -(2^4) \):
\[
- (2 \times 2 \times 2 \times 2) = -16.
\]

3. \( (-2)(-2)(-2)(-2) \):
This is the same as \( (-2)^4 \):
\[
(-2) \times (-2) \times (-2) \times (-2) = 16.
\]

4. \( 2^4 \):
\[
2 \times 2 \times 2 \times 2 = 16.
\]

Now, let's summarize the results:

- \( (-2)^4 = 16 \)
- \( -2^4 = -16 \)
- \( (-2)(-2)(-2)(-2) = 16 \)
- \( 2^4 = 16 \)

From this analysis, we see that \( -2^4 \) is the only expression that evaluates to -16. All other expressions evaluate to 16.

Thus, the answer is:

**-2^4**