Final answer:
The query relates to multiplication of powers and numbers in mathematics, involving rules for multiplying powers with the same base and the concept of integer powers, such as factorials and repeated multiplication. Consider two terms with the same base, that is, an and am. Here, the base is 'a'. When the terms with the same base are multiplied, the powers are added, i.e., am × an = a{m+n}
Step-by-step explanation:
The student appears to be seeking help with understanding the multiplication of powers and numbers in mathematics. In the information provided, the process involves factorial notation, as well as rules for multiplying powers with the same base. The rule for multiplying powers with the same base is to add the exponents, as shown by the equation xp x xq = xp+q.
Additionally, raising a number to an integer power means to multiply that number by itself as many times as the exponent indicates, as expressed in 43 being 4 x 4 x 4. Problems like these often require careful step-by-step evaluation and can sometimes involve factorial operations (such as 4!), which represents the product of all positive integers up to that number (4 x 3 x 2 x 1).
When two terms with exponents are multiplied, it is called multiplying exponents. The multiplication of exponents involves certain rules depending upon the base and the power. Sometimes we need to multiply negative exponents, or multiply exponents with the same base, or different bases. In all these cases, we follow different rules.
Before exploring the concept of multiplying exponents, let us recall the meaning of exponents. An exponent can be defined as the number of times a quantity is multiplied by itself. For example, when 2 is multiplied thrice by itself, it is expressed as 2 × 2 × 2 = 23. Here, 2 is the base, and 3 is the power or exponent. It is read as '2 raised to the power of 3'.