Graduate Management Admission Test (GMAT) Practice Test

In terms of mathematics, what does the expression (X²Y⁴) represent when raised to a power?

1. A square root function

2. A polynomial

3. A product of variables

4. A combination

The correct answer is: A product of variables

The expression \( (X²Y⁴) \) raised to a power represents a product of variables that can be expressed in a different mathematical form depending on the exponent applied. When you raise \( (X²Y⁴) \) to a power, say \( n \), you will use the properties of exponents, which state that \( (a^m b^n)^p = a^{mp} b^{np} \). Therefore, for \( (X²Y⁴)^n \), you apply the exponent \( n \) to both \( X² \) and \( Y⁴ \) individually, leading to: \[ (X²Y⁴)^n = X^{2n}Y^{4n} \] This demonstrates that the expression contains products of variable powers, reinforcing the interpretation of \( (X²Y⁴) \) as a product of variables. The other options represent different concepts: a square root function refers specifically to a function involving a square root, a polynomial typically involves a sum of terms with non-negative integer exponents, and a combination suggests a process of selecting elements from a set. Thus, the nature of \( (X²Y⁴) \)