We need to do a better job of giving kids the NEED for math. Helping my 8th grade son with his Pre-Algebra review homework tonight, we got stumped on taking negative fractions to the third power. Perhaps it because I teach in technology where everything has practical applications or maybe it's just my personality; but I cannot think of a reason to perform that calculation.
As a review section, I know to look back in the chapter for help. The original lesson explained that elephants eat 125 pounds of hay a day. We can write that as 5^3. OK, but why would you? If you asked anyone helping feed the elephant to bring you 5^3 pounds of hay, I bet the elephant would be hungry.
I understand that exponents and roots are shorthand for longer calculations. They are useful in programming as a way to reduce the size of the code. Outside of that context, I just don't get why anyone would know (or care) that a volleyball court has an area of 2^7 meters. Tell me the court is 128 square meters and that has meaning. We can cover it with carpet, or add sand to a depth and we're talking volume.
We were both long past figuring out the HOW, but I need to know the WHY. If the notation does not communicate meaning, then it becomes meaningless and our students are lost.