Can you see why the quantity gets close to one and not to zero? Thus, we would not intuitively expect 16 0 to be zero. You are not multiplying 3 times zero, you are just not multiplying by itself at all. The number 3 is not being multiplied so it remains the same.
Get a free answer to a quick problem. Most questions answered within 4 hours. Choose an expert and meet online. 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.
So, by definition, raising something to the power of zero means you start with 1, and then don't multiply it by anything. So, naturally, 1 is what you're left over with. Why any number to the zero power always gives a one? Answer 1: This is an excellent question!
Answer 2: It's exciting to me that you asked this question. Okay, enough, onto your question: Mathematics was initially developed to describe relationships between everyday quantities generally whole numbers so the best way to think about powers like a b 'a' raised to the 'b' power is that the answer represents the number of ways you can arrange sets of 'b' numbers from 1 to 'a'.
Hope this helps! Answer 3: Any number to the zero power always gives one. Answer 4: Let's look at what it means to raise a number to a certain power: it means to multiply that number by itself a certain number of times.
Answer 5: Heres a quick demonstration of why any number except zero raised to the zero power must equal 1. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math 8th grade Numbers and operations Exponents with negative bases. Exponents with negative bases. Practice: Exponents with integer bases.
Practice: Exponents with negative fractional bases. Sign of expressions challenge problems. Practice: Signs of expressions challenge. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript What I want to do in this video is think about exponents in a slightly different way that will be useful for different contexts and also go through a lot more examples.
So in the last video, we saw that taking something to an exponent means multiplying that number that many times. So if I had the number negative 2 and I want to raise it to the third power, this literally means taking three negative 2's, so negative 2, negative 2, and negative 2, and then multiplying them.
So what's this going to be? Well, let's see. Since an empty product, like an empty sum should be neutral and not affect the product of the numbers coming in after it, the multiplying machine should be set at 1 before it starts work.
Why not just take out a calculator, let her punch in any number she likes, and then let her hit square root over and over. 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.
0コメント