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Pre-algebra

Course: Pre-algebra>Unit 5

Lesson 2: Powers of whole numbers

The zeroth power

Sal Khan considers two different ways to think about why a number raised to the zero power equals one: 1) if 2^3 = 1x2x2x2, then 2^0 = 1 times zero twos, which equals 1. 2) By following a pattern of decreasing an exponent by one by dividing by the base, we find that when we get to the 0 power, we end up dividing the base by itself, resulting in 1.

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• I watched this video and it explained a lot because I didn't understand this before, but at the end of the video I realized that if you used the first method, that 0 to the power of 0 = 1. But 0 to the power of 1 = 0! Can someone please explain why that is?
• 0 to the 0th power is debated within the mathematical community. Some may say that it is 1, some may say that it is 0. Most people would just agree that it is indeterminate.
• I know that n/0 is undefined , because you can add 0 as many as times you want but you can not get n . This means that division by zero is not defined as written in my textbook . But what if we have 0 / 0 . Isn't it possible. Because you can add zero as many as times and you will always get zero . So here(in 0 /0) we are getting an answer which can be any number. So in this division by zero is defined and it is correct . And answer to this division problem is possible.
Am I right?
• Good question! The fact that 0/0 can be any number does not make 0/0 defined, because it is not a definite number. The best thing to call 0/0 is indeterminate (which means inconclusive).

If you study calculus later, you will frequently encounter indeterminate situations in limit problems.
• I know he said at to "ponder Zero to the Zeroth power", but I am curious. What other science is behind it? I have been out of 6th grade for 4 years now, but I never really got an answer when I asked around. Not even Google is really helpful. Which theory is more supported? Personal opinions? Any answer is appreciated.
• Most people say that it is indeterminate. You can get 0 or 1 if you use different solutions, but 0 is not equal to 1, so that is why it is indeterminate.
• how do you times decimals with exponets
• I don’t know 😵‍💫😬
• What is zero to the zeroth power?
• Look at previous responses, the number one voted gives a good answer.
• Since 10^0, is 1. Does this mean it is 10^1? If I am multiplying 10^0 x 10^5, we add the exponents but am I adding zero, or one? If 10^0 is equal to 10^1, then the product should be 10^6. Is this right?
• Yes, 10^0 = 1, but this is not the same as 10^1, which would equal 10.

So 10^0 x 10^5 = 10^5, not 10^6.
• are there exponents like -1
• Yes, there are negative exponents, since it is hard to explain in words (for me) I'm just going to show an example,
5^3=125
5^2=25
5^1=5
5^0=1
5^-1= 1/5 = 0.2
5^-2= .2/5 = 0.04
• This is a very good question! Consider the following two rules:

1) Zero to any positive power is 0.
2) Any nonzero number to the zero power is 1.

If we try to extend both rules to define 0^0, we get different answers. It is unclear if 0^0 should be 0, 1, or something else. Because of this, it is best to call 0^0 indeterminate (though 0^0 is often interpreted as 1).
• hello people i have a question what's -1^0?
• When evaluating the expression -1^0, it is important to consider the order of operations. In mathematics, exponentiation takes precedence over negation. Therefore, the exponentiation is performed before applying the negative sign.

Applying the exponent of 0 to -1 gives us:

-1^0 = (-1)^0

Any non-zero number raised to the power of 0 is defined as 1. Therefore:

(-1)^0 = 1

So, the value of -1^0 is 1, not -1.