# beginning algerbra

#### earlbrewer

##### New member
powers of (0) zero does it always = 1 : negitive two thirds with zero power i got -1

#### tkhunny

##### Moderator
Staff member
One has only to use zero to disprove the conjecture that it's always zero.

$$\displaystyle 0^{0}\;\ne\;1$$

How did you get -1? That must have been quite an adventure.

#### mmm4444bot

##### Super Moderator
Staff member

Perhaps you entered it wrongly into some calculator?

For example, if you enter -4^0 into a calculator that's been designed to follow the Order of Operations, you will get -1, and that is correct.

If you enter (-4)^0, then you will get 1.

Likewise,

$$\displaystyle \left(-\frac{2}{3}\right)^{0} = 1$$

$$\displaystyle -\left(\frac{2}{3}\right)^{0} = -1$$

At the beginning-algebra level, the rule is "every Real number raised to the power of zero equals 1".

When you enter advanced-algebra or precalculus courses, this rule changes somewhat to "every Real number raised to the power of zero equals 1 except for 0^0, which is called an indeterminant form". (This is because mathematicians have not settled on a definite meaning for the expression 0^0.)

So, at your current level of studies, I say that 0^0 = 1. Additional inquiries about this should be directed to your instructor, if you desire further insight with respect to your course.

Cheers 