Final answer:
The quotient rule allows negative exponents to be converted into positive exponents by flipping the base into the denominator, such as x^-n becoming 1/x^n.
Step-by-step explanation:
The property that allows you to rewrite expressions with negative exponents to positive exponents is C) Quotient rule. The quotient rule in the context of exponents states that when you have a negative exponent, you can invert the base and make the exponent positive. An example of this property is observing that x-n = 1/xn, meaning that a negative exponent implies a division rather than multiplication. In symbolic form, we can express the rule as x-n = 1 / xn, where x is the base and n is a positive integer.
To provide a detailed explanation, let's consider an example: when manipulating the expression 3-4, applying the quotient rule would lead us to rewrite it as 1/34. In this scenario, the base 3 is raised to a power of -4. By the quotient rule, we create a fraction with a numerator of 1 and the base raised to a positive 4 in the denominator, flipping the negative exponent to a positive one. The same approach can be applied generally to any negative exponent expression to convert it to an equivalent expression with positive exponents.Understanding this concept is crucial for simplifying algebraic expressions and solving equations involving exponents, particularly when they are part of more complex algebraic operations including multiplication, division, and raising to powers.