Graduate Management Admission Test (GMAT) Practice Test

Which mathematical expression represents the law of exponent multiplication correctly?

1. (x + y)^z

2. (x - y)^z

3. xy * z

4. (xy)^z

The correct answer is: (xy)^z

The law of exponent multiplication states that when multiplying two powers with the same base, you can add their exponents. In the context of the provided choices, the correct representation showcases the ability to raise a product to a power. The expression that accurately reflects this law is (xy)^z, which indicates that the product of x and y is raised to the zth power. This means you would expand it to x^z * y^z, clearly aligning with the exponent multiplication law. This demonstrates that the multiplication of the bases (x and y) results in the addition of their exponents when raised to a power. The other expressions fail to illustrate the correct application of the law. For instance, (x + y)^z and (x - y)^z represent the sum or difference of x and y raised to the power of z, which does not align with the exponent rules pertaining to multiplication. Similarly, xy * z does not use exponent notation and represents simple multiplication rather than exponentiation, reinforcing that it does not adhere to the principle of exponent multiplication. Thus, the only choice that correctly represents the law of exponent multiplication is (xy)^z.