Understanding when to add or multiply exponents hinges on recognizing the rules of exponents. When multiplying like bases, such as in (a^2)(a^3), the exponents add, resulting in a^5. Conversely, raising a power to another power, like (a^3)^2, multiplies the exponents, yielding a^6. Visualizing this with binary representations can aid in grasping the concept, particularly with powers of 2, where multiplication corresponds to shifting left in binary form. Ultimately, consistent practice and application of these rules will lead to better intuition and understanding of exponent manipulation.