Final answer:
The expression m⁹ * m⁻⁹ equals 1 because when you multiply expressions with the same base, you add the exponents, leading to m⁰, which is always equal to 1 for any non-zero base. The correct answer is option C. 1
Step-by-step explanation:
The answer to the question which of the following is equal to m⁹ * m⁻⁹ is C, which is 1. We use the laws of exponents to solve such problems, specifically when multiplying expressions with the same base, we add the exponents. In this case, we have m raised to the power of 9 (m⁹) multiplied by m raised to the power of negative 9 (m⁻⁹). According to the laws of exponents:
m⁹ * m⁻⁹ = m¹⁹ + (⁻⁹) = m⁰
Anything to the power of 0 is 1, therefore:
m⁰ = 1
This holds true for any non-zero value of m, as the exponent rules are applicable for all non-zero bases. It is important to note that these laws are foundational and are typically introduced at the middle school level and reinforced throughout high school mathematics courses.