Graduate Management Admission Test (GMAT) Practice Test

If (X²Y⁴)³ is simplified, what is the result?

1. X⁶Y⁶

2. X⁴Y¹²

3. X⁶Y¹²

4. X²Y⁸

The correct answer is: X⁶Y¹²

To simplify the expression \((X²Y⁴)³\), you can apply the power of a product rule, which states that \((a \cdot b)^n = a^n \cdot b^n\). In this case, \(X²\) and \(Y⁴\) are the components of the product. First, distribute the exponent of 3 across the terms inside the parentheses: \[ (X²Y⁴)³ = (X²)³ \cdot (Y⁴)³ \] Next, apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\): For \(X²\): \[ (X²)³ = X^{2 \cdot 3} = X^6 \] And for \(Y⁴\): \[ (Y⁴)³ = Y^{4 \cdot 3} = Y^{12} \] Now, combine the simplified terms: \[ (X²Y⁴)³ = X^6 \cdot Y^{12} \] So, the final result is \(X^6Y^{12}\).