Which expression is equivalent to a 11 ⁄ 12 , where a 0?

Question

Which expression is equivalent to a 11 ⁄ 12 , where a > 0?

Accepted Answer

Choice B is correct. Since 12 ⁄ 12 = 1, multiplying the exponent of the given expression by 12 ⁄ 12 yields an equivalent expression: a ( 11 ⁄ 12 )( 12 ⁄ 12 ) = a 132 ⁄ 144 . Since (132)( 1 ⁄ 144 ) = 132 ⁄ 144 , the expression a 132 ⁄ 144 can be rewritten as a (132)( 1 ⁄ 144 ) . Applying properties of exponents, this expression can be rewritten as (a 132 ) 1 ⁄ 144 . An expression of the form (m) 1 ⁄ k , where m > 0 and k > 0, is equivalent to k √ m . Therefore, (a 132 ) 1 ⁄ 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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