Sounds stupid, but it's bugging the hell out of me. All through high school we were taught that a negative number raised to an even power came out to be a positive number (-4 squared = -4*-4 = 16). However, today was my second day of college and I'm almost positive I just learned that a negative number raised to any power, odd or even, always results in a negative number.

Have I been lied to all these years, or did I just misinterpret my professor?

edit - I just opened my new calculator and punched in an equation, and to my surprise it came out negative. This leads me to believe my high school teachers had us change the format on our calculators so answers would come out different.

Why would this be taught two completely different ways? What is the logic behind this? Surely one way has to be wrong. -2^2 can't = 4 and -4.

(-2)^2 is 4. -2^2 is -4. lern2orderofoperations.

However, that really only explains your calculator. I don't know why they would be teaching you in college that a negative number raised to any power is still negative.

Any number with a exponent that it divisible by 2 gives a positive answer. If the exponent is negative, you get a negative answer.


So (-2)^5 or 7 or 9 etc. is the same as 2^5/7/9

and 2^2/4/6/8/10 is positive, same as (-2)^2/4/6



If you give -2^2 into your calculator it calculates 2^2 and then just adds the minus back.
(-2)^2 would be the correct way to calculate it and you'll see that the answer is positive; (+)4 .

If the exponent is negative, you get a negative answer.

No, a negative exponent just means to take the reciprocal of its positive exponent.

Example:

2^-2 = 1/(2^2) = 1/4

anyway - let's say in boxing you have to be punched an even amount so you don't have amnesia (even exponent = result is always positive)

but if you get punched an odd amount of times, you have amnesia (odd exponent = result may be negative)

2^2 = 4

(-2)^2 = 4

(-2)^3 = -8

Your high school taught you correctly.

The reason your calculator gave you a -4 was because you didn't use parentheses.

(-2)^2 = 4

-(2^2) = -4

Your calculator interprets it the second way if you use no parentheses.