Graduate Management Admission Test (GMAT) Practice Test

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What is the result of the expression (n/m)ˉᵃ?

(m/n)ᵃ = mᵃ/nᵃ
(n/m)ᵃ = m/n
nˉᵃ/mˉᵃ
((n/m)ᵃ)ˉ

The correct answer is: (m/n)ᵃ = mᵃ/nᵃ

The expression (n/m)ˉᵃ represents the reciprocal of (n/m) raised to the power of a. When you raise a fraction to a negative exponent, the negative exponent signifies taking the reciprocal of the fraction first, and then applying the positive exponent. To break it down: 1. The expression can be rewritten as 1/(n/m)ᵃ. 2. When dealing with fractions, taking the reciprocal of (n/m) gives you (m/n). 3. Then, raising (m/n) to the power of a results in (m/n)ᵃ. Therefore, the correct transformed expression is (m/n)ᵃ, which can also be rewritten as mᵃ/nᵃ, demonstrating the application of the power of a fraction rule. This follows the mathematical property that states (a/b)ᵃ = aᵃ/bᵃ, so when applying the negative exponent, we confirm that (n/m)ˉᵃ indeed simplifies correctly to (m/n)ᵃ, which is equivalent to mᵃ/nᵃ. This makes sense in the context of exponents and fraction manipulation in algebra.