Question

Which expressions are equivalent to 1 • 1 • 1 •
1 ?
2 2 2 2
(choose 2)
Responses
A
1
8
1 8
B
( 1 )-4
2
( 1 ) -4 2
C 2-2 • 2-22 -2 • 2 -2
D 242 4
E
1
24

Answer 1

To determine which expressions are equivalent to \( 1 \cdot 1 \cdot 1 \cdot 1 \) and \( 2^2 \cdot 2^2 \), we can simplify both to see what they equal.

1. The expression \( 1 \cdot 1 \cdot 1 \cdot 1 \) simplifies to 1.

2. The expression \( 2^2 \cdot 2^2 \) simplifies to \( 2^{2+2} = 2^4 = 16 \).

Now, we need to evaluate the given choices:

- A: \( 1, 8 \) (not equivalent to 1 or 16)

- B: \( (1)^{-4} = 1 \) and \( 2^{(-4)} = \frac{1}{16} \) (equivalent to 1 but not 16)

- C: \( 2^{-2} \cdot 2^{-2} = 2^{-2-2} = 2^{-4} = \frac{1}{16} \) (not equivalent)

- D: \( 2^{42} \, 4 \) (not equivalent, likely a typo)

- E: \( 1, 24 \) (not equivalent to 1 or 16)

Thus, the expressions that are equivalent to \( 1 \) (but none to \( 16 \)) are:

- **A**: Identifies \( 1 \)
- **B**: Identifies \( 1 \)

Final answer, to the question, two correct choices based on \( 1 \) would be **A** and **B**. Only **B** also satisfies the \( 2^{-4} \) reaching \( \frac{1}{16} \) but none exactly fulfill \( 16 \).

If we are to strictly represent possible selections:

Thus, the two expressions equivalent to **1 are**:
- **A: 1**
- **B: (1)^{-4}**