Final answer:
The associative property of multiplication is used to show that 5² is equivalent to √5³ by indicating that 5×(√5×√5) simplifies to √5³.
Step-by-step explanation:
The question is asking which mathematical property can be used to show that the expression 5² is equivalent to √5³. To understand this equivalence, we can interpret 5 as the square root of 5, since multiplying it by itself yields 5. Therefore, we express this as a fractional power: x² = √x. The correct property that allows us to go from 5² to √5³ is the associative property of multiplication (not to be confused with the associative property of addition). The associative property in multiplication allows us to regroup factors without changing the product.
Using this property, we start with 5² which is 5×5. Then we can think of this as 5×(√5×√5), where √5 is the square root of 5. This indicates that 5² is indeed equivalent to √5³.