Graduate Management Admission Test (GMAT) Practice Test

If you multiply x^a by x^b, what is the result?

1. x^(a - b)

2. x^ab

3. x^(a + b)

4. x^a + x^b

The correct answer is: x^(a + b)

When you multiply expressions that have the same base, you add the exponents. This is a fundamental property of exponents in mathematics. In this case, when you multiply \(x^a\) by \(x^b\), you apply this property: \[ x^a \cdot x^b = x^{a + b} \] Thus, the result of multiplying \(x^a\) by \(x^b\) is \(x^{a + b}\). This shows the correct application of the laws of exponents, making choice C the right answer. In contrast, the other options represent operations or expressions that do not conform to the rules of exponents for multiplication. Option A suggests a subtraction of exponents, which is incorrect for multiplication. Option B implies that the exponents should be multiplied, which also does not apply in this situation. Option D implies adding the terms rather than the exponents, which again does not follow the correct multiplication process of exponents.