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12 a^11 Which expression is equivalent to, a > 0 where? 12 a^132
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
12 =1 Choice B is correct. Since 12 , multiplying the exponent of the given expression by 1 1 2 2 yields an equivalent expression: a c1 1 2 1 mc1 1 2 2 m= ac1 1 4 3 4 2 m. Since 1 1 4 3 4 2 =132 b 14 1 4 l, the expression a 1 1 4 3 4 2 can be rewritten as a^ 132 hc14 1 4m. Applying properties of exponents, this 1 132 144 1 expression can be rewritten as ^a h . An expression of the form ^mh k, where 1 m > 0 and k > 0, is equivalent to k m. Therefore, ^a 132 h 144 is equivalent to 144 a 132 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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