What are the rules for multiplying exponents?

When multiplying exponents that have the same base, the correct rule to apply is to add the exponents together. This principle arises from the definition of exponents, which states that when you multiply two powers with the same base, you can combine them by adding their exponents. For example, (a^m \times a^n) can be rewritten as (a^{m+n}).

This rule allows for simplification and is a foundational concept in exponent rules, illustrating how exponential growth works when the same base is involved. Recognizing this principle is crucial for solving more complex problems involving exponential expressions in mathematics and science.

The other choices do not accurately reflect the rules for manipulating exponents. Subtracting exponents is applicable in the case of division, not multiplication; multiplying numbers before applying exponents is not a standard practice in exponent rules; and multiplying by zero does not relate directly to the rules of exponents in a meaningful way. Hence, the understanding that one must add exponents when the bases are the same is central to using exponents correctly in mathematical operations.