Graduate Management Admission Test (GMAT) Practice Test

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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!

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What is the expression for (x^a)^b?

x^(a + b)
x^a x x^b
x^ab
x^(a - b)

The correct answer is: x^ab

The correct expression for (x^a)^b is x^(ab). This result arises from the laws of exponents, specifically the power of a power rule. When you raise a power to another power, you multiply the exponents. In this case, when you take x raised to the power of a and then raise that entire expression to the power of b, you multiply a and b together, resulting in x raised to the power of ab. This principle can be illustrated with a simple example: if a is 2 and b is 3, then (x^2)^3 = x^(2*3) = x^6. This confirms the application of the exponent rule and reinforces that the correct result is indeed x^(ab).