To determine which pairs of expressions are equivalent, let's evaluate each pair step by step.
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Pair: (43)³ and 43 ⋅ 43
- (43)³ = 43 × 43 × 43 = 43 ⋅ 43 ⋅ 43
- These expressions are equivalent.
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Pair: (34)⁴ and 38 ⋅ 38
- (34)⁴ = 34 × 34 × 34 × 34
- 38 ⋅ 38 = 38²
- These expressions are not equivalent.
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Pair: 64 ⋅ 34 and 188
- 64 × 34 = 2176
- 188 is simply 188
- These expressions are not equivalent.
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Pair: 43 ⋅ 53 and 203
- 43 × 53 = 2279
- 203 is simply 203
- These expressions are not equivalent.
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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.