In this clip the teacher leads a discussion about what makes a situation exponential.
Introduction to Exponential Functions, Clip 5, 2:17
The teacher introduces the notion of 3 to the 1/2 power and the students appear to realize that this is NOT the same thing at 3 multiplied by 1/2. This is the first time in this class they have discussed non-integer exponents.
The teacher uses the terminology for the class by using the term factor when discussing this situation. She uses the phrase 1/2 factors of 3.
She helps reinforce the notion of factor and the meaning of 1/2 as an exponent by having them think about how many 1/2 factors of 3 are needed to get 3. This can aid in the students transition to non-integer exponents.