If ( √n ⁄ n –1/2 )m = 5, what is the value of m in terms of n?

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The denominator of the fraction has a negative exponent: n –1/2 . It can be placed in the numerator with a positive exponent, since 1 ⁄ n –1/2 = n 1/2 . The numerator of the fraction is now (n 1/2 )(n 1/2 ) and the denominator of the fraction is 1. To multiply terms with like bases, keep the base and add the exponents: (n 1/2 )(n 1/2 ) = n. Therefore, nm = 5, and m = 5 ⁄ n .

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