Graduate Management Admission Test (GMAT) Practice Test

What is the result of simplifying the expression (x²)ᵇ?

1. x²b

2. (x)b²

3. xy where y = b

4. x^(2b)

The correct answer is: x^(2b)

To simplify the expression (x²)ᵇ using the properties of exponents, you apply the power of a power rule, which states that (a^m)ⁿ = a^(m*n). In this case, x² is raised to the power of b. By applying this rule: 1. Identify the base, which is x, and the exponent, which is 2. 2. When you raise x² to the power of b, you multiply the exponents: 2 (from x²) and b. 3. This results in x^(2*b), which can be written as x^(2b). Thus, the simplified result of (x²)ᵇ is indeed x^(2b), confirming that the correct answer is x^(2b). This expression maintains the integrity of the original terms while adhering to the exponent rules, making this approach valid and mathematically sound.