Why is exponent to zero 1

No matter what number we use when it is raised to the zero power it will always be 1. Suppose instead of 3 we used some number N, where N could even be a decimal. Heres a quick demonstration of why any number except zero raised to the zero power must equal 1. As an example we will let that any number be the number 3.

This same reasoning will work for any number not just 3 , except the number 0. It wont work for 0 because you cant divide by 0. Lets call any number x:. Raising something to a power greater than zero means multiplying it by itself a number of times equal to the power. So, for instance,. Now, you can multiply anything by 1 and it will still be the same thing, and likewise you can divide anything by 1 and it will still be the same.

Now, also note that if you raise something to a negative power, then you take the reciprocal of that something:. Well, you're not multiplying by anything, except the 1 you started with. You're not dividing by anything, except the 1 you started with. So, what you're left over with is 1. Now, here is the slightly more mathematically sophisticated version: when you raise something to a power, what you do is take 1 and multiply it by the base of the power a number of times equal to the power.

Don't give up - it's there. Take a look at this url - it presents a more thorough understanding of exponents; it goes beyond the conventional explanation i. Once you have the intuitive understanding, you can use the simple rules with confidence. As a more simple approach for someone like me who was trying to get to the depths of this question as I'm trying to learn binary and programming.

Differentiating the process by which we calculate something as to that which a process or calculation actually means might be important. I think this sort of approach without going into too much depth is counter intuitive as it will where the mind is eager warrant further thought and possible investigation into mathematical system, structures and origins Try thinking in terms other than math.

Tell her to take any number of balls that are the same size. Take each one and stack them vertically on a table. Tell her to look down and tell you how many balls do you see? Tell her the top of the table equals the power of zero. Then tell her to lower her head to the level of the table. Then ask her to tell you how many balls do you see now? This will always stay in her mind whenever this is used in any equation in the future.

Math by Association by Bill R. Association is a wonderful tool to use with any age. I hope this is helpful. Let's consider, their is 1bacteria in a dish.

It doubles every hour i. You have 1 dollar. Assume it triples every day i. Remember, if their is no bacteria or no money,that means it cant multiply. If u still have doubt 'what will we do if we have 3dollar at the start itself?

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How do I explain 2 to the power of zero equals 1 to a child Ask Question. Asked 11 years ago. Active 6 years ago. Viewed k times. So suppose we don't know what -3 0 is. Whatever -3 0 is, if it obeys the rule above, then.

Since we are supposing that we don't yet know what -3 0 is, let's substitute P for it. Now look at the equations we found above. Knowing what you know about properties of multiplication, what kind of number can P be? What is the difference between -1 to the zero power and -1 to the zero power? Will the answer be 1 for both? Answer: As already explained, the answer to -1 0 is 1 since we are raising the number -1 negative 1 to the power zero. However, in the case of -1 0 , the negative sign does not signify the number negative one, but instead signifies the opposite number of what follows.

So we first calculate 1 0 , and then take the opposite of that, which would result in Another example: in the expression - -3 2 , the first negative sign means you take the opposite of the rest of the expression. Exponents are important in the financial world, in scientific notation, and in the fields of epidemiology and public health. So what are they, and how do they work?

The "3" here is the base , while the "2" is the exponent or power. Now that we have some understanding of how to talk about exponents, how do we find what number it equals?

The left-most number in the exponent is the number we are multiplying over and over again. That is why you are seeing multiple 3's. The right-most number in the exponent is the number of multiplications we do. So for our example, the number 3 the base is multiplied two times the exponent.

For these examples above, the exponent values are relatively small. But you can imagine if the powers are very large, it becomes redundant to keep writing the numbers over and over again using multiplication signs.