Graduate Management Admission Test (GMAT) Practice Test

Disable ads (and more) with a membership for a one time $2.99 payment

Prepare for the GMAT exam with flashcards and multiple choice questions. Each question includes hints and explanations. Enhance your readiness and boost your confidence before your test!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

Practice this question and more.

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.