What is the rule for adding exponents with the same base?

When you are working with exponents that have the same base, the established mathematical rule is to add the exponents together. This is a fundamental property of exponents, known as the product of powers property.

For example, if you have (a^m \times a^n), where (a) is the base and (m) and (n) are the exponents, you can combine them into a single term by adding the exponents: (a^m \times a^n = a^{m+n}). This rule shows that when multiplying like bases, you effectively combine their powers by summing the exponents. This principle applies regardless of whether the exponents are positive, negative, or zero, as long as the bases remain the same.

Understanding this property allows for easier manipulation of expressions involving exponents in algebra. For students practicing the PSAT, recognizing and applying this rule correctly is crucial for solving various types of problems they may encounter on the test.