The mathematical principle that addresses exponents of expressions involving multiplication dictates that raising a product to a power is equivalent to raising each factor to that power individually. For instance, consider (ab)n. This is mathematically identical to anbn. A numerical illustration is (2 3)2, which equals 62 or 36. This result can also be obtained by computing 22 32, yielding 4 * 9, which again equals 36.
This property simplifies complex calculations and is fundamental to algebraic manipulation. Its application allows for efficient problem-solving in various fields, including engineering, physics, and computer science. Historically, the understanding and application of this concept facilitated advancements in mathematical notation and paved the way for more complex algebraic structures.
