Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

When multiplying numbers with exponents, what operation should you perform with the exponents?

1. Multiply them

2. Add them

3. Subtract them

4. Leave them unchanged

The correct answer is: Add them

When multiplying numbers with exponents that have the same base, you should add the exponents. This is a fundamental property of exponents known as the product of powers rule. For example, if you have \( a^m \times a^n \), you combine the exponents by adding them together, resulting in \( a^{m+n} \). This rule applies only when the bases are the same. Therefore, if you were to multiply different bases or apply it in different contexts, the operation might change. Understanding this operation helps simplify expressions and perform calculations involving exponents more efficiently in algebra.