Question

Select all the pairs of equivalent expressions.
(43)3 and 43 ⋅
43
(34)4 and 38 ⋅
38
64 ⋅
34 and 188
43 ⋅
53 and 203
(43)3 and 43 ⋅
43 ⋅
43

Answer 1

To determine which pairs of expressions are equivalent, let's evaluate each pair step by step.

1. **Pair: (43)³ and 43 ⋅ 43**
- (43)³ = 43 × 43 × 43 = 43 ⋅ 43 ⋅ 43
- These expressions are equivalent.

2. **Pair: (34)⁴ and 38 ⋅ 38**
- (34)⁴ = 34 × 34 × 34 × 34
- 38 ⋅ 38 = 38²
- These expressions are not equivalent.

3. **Pair: 64 ⋅ 34 and 188**
- 64 × 34 = 2176
- 188 is simply 188
- These expressions are not equivalent.

4. **Pair: 43 ⋅ 53 and 203**
- 43 × 53 = 2279
- 203 is simply 203
- These expressions are not equivalent.

5. **Pair: (43)³ and 43 ⋅ 43 ⋅ 43**
- (43)³ = 43 × 43 × 43 = 43 ⋅ 43 ⋅ 43
- These expressions are equivalent.

From the analysis, the pairs of equivalent expressions are:

- (43)³ and 43 ⋅ 43 ⋅ 43

Thus, the equivalent pairs are:

- (43)³ and 43 ⋅ 43 ⋅ 43

The only equivalent pairs are the first and the last pairs.