Graduate Management Admission Test (GMAT) Practice Test

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

1. x^(a + b)

2. x^a x x^b

3. x^ab

4. 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).