Graduate Management Admission Test (GMAT) Practice Test

What is the simplified form of (a⁴b²)²?

1. a⁸b⁴

2. a⁶b³

3. a²b²

4. 2a⁴b²

The correct answer is: a⁸b⁴

To determine the simplified form of \((a^4b^2)^2\), you can apply the power of a product rule, which states that when raising a product to a power, you must raise each factor to that power. Starting with the given expression: \[ (a^4b^2)^2 \] You distribute the exponent of 2 to both \(a^4\) and \(b^2\). This means you calculate: \[ a^{4 \cdot 2} \text{ and } b^{2 \cdot 2} \] Calculating these gives: \[ a^{8} \text{ and } b^{4} \] Now combine these results: \[ a^8b^4 \] Thus, the simplified form of \((a^4b^2)^2\) is indeed \(a^8b^4\), making it clear why this choice is the correct answer. The expression is simplified accurately by applying the laws of exponents appropriately.