To determine which property best describes the equation [tex]\( a / b = c / d \)[/tex] and its equivalence to [tex]\( ad = bc \)[/tex], let's explore each property mentioned:
1. Cross Product Property:
- This property states that for real numbers [tex]\( a, b, c \)[/tex], and [tex]\( d \)[/tex] (where [tex]\( b \)[/tex] and [tex]\( d \)[/tex] cannot equal zero), the equation [tex]\( a / b = c / d \)[/tex] is equivalent to [tex]\( ad = bc \)[/tex]. This means that if two ratios are equal, then their cross products are also equal.
2. Exponent Property:
- This property involves operations with exponents, such as [tex]\( a^m \cdot a^n = a^{m+n} \)[/tex] or [tex]\( (a^m)^n = a^{mn} \)[/tex]. It is not related to the relationship between two ratios.
3. Reflexive Property of Equality:
- This property states that any quantity is equal to itself, such as [tex]\( a = a \)[/tex]. It does not provide any information about the relationship between two different ratios.
4. Square Root Property of Equality:
- This property states that if [tex]\( a^2 = b \)[/tex], then [tex]\( a = \pm\sqrt{b} \)[/tex]. It deals with the square roots of a number and their equality, not with the ratios of numbers.
Given these definitions, the appropriate property that describes the equation [tex]\( a / b = c / d \)[/tex] being equivalent to [tex]\( ad = bc \)[/tex] is the Cross Product Property.
Thus, the property best describing the given equation is:
Cross Product Property
