Question

Which expressions are NOT equivalent to 1 • 1 • 1 •
1 •
1 ?
3 3 3 3 3
(choose 3)
Responses
A 353 5
B
( 1 )-5
3
( 1 ) -5 3
C 3-3 • 3-23 -3 • 3 -2
D
1
3-5
1 3 -5
E
1
243
1 243

Answer 1

To determine which expressions are NOT equivalent to \(1 \cdot 1 \cdot 1 \cdot 1 \cdot 1 = 1\), we need to analyze each option.

1. **Option A: \(353^5\)**
- This is a real number raised to a power and is definitely not equal to 1, so it is NOT equivalent.

2. **Option B: \((1)^{-5} \cdot 3 \)**
- \((1)^{-5} = 1\), thus it simplifies to \(1 \cdot 3 = 3\); this is NOT equivalent to 1.

3. **Option C: \(3^{-3} \cdot 3^{-2}\)**
- This simplifies to \(3^{-3-2} = 3^{-5}\). \(3^{-5}\) is a real number (specifically, \(1/243\)) which is not equal to 1, so this is NOT equivalent.

4. **Option D: \(\frac{1}{3^{-5}}\)**
- This simplifies to \(1 \cdot 3^5 = 243\) which is not equal to 1, thus it is NOT equivalent.

5. **Option E: \(\frac{1}{243}\)**
- This is simply \( \frac{1}{243}\), which is NOT equal to 1.

Thus, the expressions that are NOT equivalent to \(1\) are:
- A: \(353^5\),
- B: \((1)^{-5} \cdot 3\),
- C: \(3^{-3} \cdot 3^{-2}\),
- D: \(\frac{1}{3^{-5}}\),
- E: \(\frac{1}{243}\).

To select three, we could choose any three from A, B, C, or D. A viable set is:
1. A
2. B
3. C

So these three expressions are NOT equivalent to \(1\).