The laws of indices, also known as the laws of exponents or the rules of exponents, are mathematical rules that govern the manipulation and simplification of expressions involving powers or exponents. These laws are used extensively in algebra and provide a systematic way to simplify and perform operations on exponential expressions. Here are the basic laws of indices: Product Rule: For any positive real numbers a and b, and any integer n: a^n * a^m = a^(n + m) In words, when multiplying two...