Exponentially Speaking

Louis Bailey is on a mission.

It started in Calculus yesterday. All over something that he hadn't quite picked up on before.

Mr. Newcomb was in the middle of something or other that was taking two-and-a-half boards to prove when he said the fatal sentence.

"And 8 to the power zero is, of course, one."

Louis's hand slid silently into the air behind Newcomb's back. Oblivious to the tempest brewing in the seat next to mine, Mr. Newcomb went on scratching out numbers and letters across the board, working towards a full three.

Louis never dealt well with being ignored.

There was the telltale scrape of his chair being pushed back and he stood at his desk, clearing his throat meaningfully as he rose. Every other body in the class straightened in its chair. They knew the signs by now.

Newcomb turned and was noticeably taken aback by the sight of a student standing at attention in his classroom.

"Yes, Mr. Bailey?"

"Pardon me, Mr. Newcomb, but could you please remind me what an exponent is?"

Convinced that he had a smart alec on his hands, Mr. Newcomb put down his chalk and crossed his arms.

"Do you mean to tell me, Mr. Bailey, that you've made it all the way to Calculus without knowing what an exponent is?"

"No, Mr. Newcomb. Of course not. I just want to clarify something. Would you please just explain what an exponent is? Just to make sure I'm not mistaken."

Rolling his eyes, Mr. Newcomb rattled off his response. "Exponents tell how many times a number is multiplied by itself. Five to the exponent two is five times five. Six to the exponent four is six times six times six times six times six. Does that refresh your memory?"

Louis nodded thoughtfully. "That rings a bell."

Mr. Newcomb turned back towards the board thinking the discussion was over, but Louis wasn't finished.

"Then how could eight to the power zero be one?"

"Pardon me?"

"Well, according to what you just told me about exponents, eight to the exponent zero would be eight times itself zero times. That would be nothing. So how could it be one?"

Again the teacher crossed his arms. "Well, Mr. Bailey, you'll recall that when you divide exponential numbers with a common base, you subtract the exponents. Five to the power six divided by five to the power four is five to the power two. Do you agree with that?"

Louis was polite enough to think it through, just to be sure.

"Yes, I agree."

"Well, then eight to the power of five divided by eight to the power of five would be eight to the power zero. Do you agree with that?"

"Yes, I agree."

"And any number divided by itself is one. Do you agree with that?"

"Yes, I agree with that."

"And, just to confirm it, Mr. Bailey, do you agree that eight to the power of five and eight to the power of five are, in fact, the same number?"

"Of course."

"Then that, Mr. Bailey, is why eight to the power of zero is one."

"I see," said Louis.

"Then we are in agreement, Mr. Bailey?"

"No, Mr. Bailey, I don't think we are."

Mr. Newcomb was clearly annoyed at this point, having thought he had proven his point adequately.

"Why not?"

"You see," said Louis evenly, "you still haven't explained to me adequately what exponents are. If, like you said, the exponent tells us how many times a number is multiplied by itself, then eight to the power zero cannot be one. It would have to be zero."

That was when Mr. Newcomb got a little huffy, said that the rest of the class probably didn't want to waste their time listening to a meaningless debate, told Louis to sit down, and went back to his blackboard proof.

I doubt anyone could have cared less. They knew they'd just witnessed the start of a new campaign.