Absolutely.  Coming up with short cuts or goofy ways to describe and perform mathematical operations (like I've seen in all too many "math" books) only shows the lack of understanding of the subject, and fails miserably in general case applications.

For a number being raised to a power, the power (which is called an exponent) can be a positive or negative real number, fraction, trig function, complex number, expression, etc.  To be using the exponent in a multiplication operation associated with the number involves the use of a property of logarithms, which is beyond the scope of where they are.

I hope the math book being used wasn't written by someone who flunked basic math and gives worthless info that will only confuse the kids later when they encounter more advanced math and then realize they were taught wrong in grade school and HS.