What does the power rule of exponents state when multiplying exponents?

• A. Add the bases
• B. Multiply the coefficients
• C. Add the exponents
• D. Subtract the exponents

Answer: (C)

The power rule of exponents states that when you multiply two expressions with the same base, you add the exponents. This means that if you have a base ( a ) raised to an exponent ( m ) and another expression with the same base ( a ) raised to an exponent ( n ), the operation can be expressed as:

[ a^m \times a^n = a^{m+n} ]

This fundamental property simplifies calculations involving exponents significantly and is crucial for algebraic operations involving polynomial expressions. For example, if you multiply ( x^3 ) and ( x^2 ), applying the power rule allows you to combine the expressions directly to get ( x^{3+2} = x^5 ). Understanding this rule is essential for successfully manipulating and simplifying equations in a variety of mathematical contexts.