Cameron Buie Zarkonnen Zarkonnen 6 6 silver badges 8 8 bronze badges. If the exponent is negative, you are throwing the factors off of the implicit 1 i. Add a comment. From there, you can segue into negative exponents, if you'd like.
Just keep dividing by 2. But I was an odd kid who enjoyed formal logic and whose idea of fun was teaching my little sister simultaneous equations. She's now doing a maths PhD. Raphael Raphael 2, 21 21 silver badges 34 34 bronze badges. This is also the only way to wrap your head around negative powers. Incidentally, the best way to teach fractions is by having pizza for dinner. Rasmus MrGlass MrGlass 1 1 silver badge 4 4 bronze badges. When this occurred to me as an adult, I couldn't help but wonder if students who frequently ate pizza specifically, the round pie, cut into 8 sections thru the center developed better number sense.
The best we can do is to convince a child of the following facts: 1. Some of the other answers provide good ways to convince a child of these facts. Compare this to the following. BusyAnt 2 2 silver badges 14 14 bronze badges.
Tsuyoshi Ito Tsuyoshi Ito 1, 11 11 silver badges 18 18 bronze badges. Just write it out for some small values of a,b. I didn't come up with "convince a kid"; that's in direct response to " I do not think that it is possible to convince a child ". This can all be done using positive integers, it doesn't even need fractions or negative numbers. It's undefined by default. Show 2 more comments. Ross Millikan Ross Millikan k 26 26 gold badges silver badges bronze badges.
Asaf Asaf 4 4 bronze badges. Said identity should be true for any base. It isn't intuitive to their world view, and abstractions are at times challenging for people, especially kids. Anyway, my daughter is now 14 and I think gets it. I up-voted your answer, it is a valid approach, and more clearly stated than the comment, although I might think about reordering it, depending which part of those steps they intuitively find agreement with. Matt Calhoun Matt Calhoun 4, 27 27 silver badges 51 51 bronze badges.
Winther Sunny Sunny 1 1 1 bronze badge. Bill R Bill R 1. You can say that combining to no number i. No number is no number. Person Person Rakesh S Rakesh S 1 1 1 bronze badge. I think you can improve the quality of your posts by being a bit more formal. Avoid using 'u' in place of 'you'. It is a good idea to start each sentence with a capital letter. Lastly, try to use TeX to render math.
Upcoming Events. Since 1 is the multiplication identity, the product is never changed by multiplying by 1. When we multiply numbers, we can start with a 1 identity and then multiply it by the rest of the numbers, just like when we add or subtract numbers, we can start with 0 identity , and then move to the right addition or left subtraction on the number line. Now consider that an exponent power is merely the number of times you need to multiply the base the five ; and don't forget to also multiply by one 1.
Now, move the 5 in the denominator to the numerator. Now, you have a product of a base raised to different powers. So clearly these are the same number. Here we just took this, and we're just multiplying it by 1, so you're still going to get negative 8. And this might be a slightly more useful idea to get an intuition for exponents, especially when you start taking things to the 1 or 0 power.
So let's think about that a little bit. What is positive 2 to the-- based on this definition-- to the 0 power going to be equal to? Well, we just said. This says how many times are going to multiply 1 times this number? So this literally says, I'm going to take a 1, and I'm going to multiply by 2 zero times. Well, if I want to multiply it by 2 zero times, that means I'm just left with the 1. So 2 to the zero power is going to be equal to 1.
And, actually, any non-zero number to the 0 power is 1 by that same rationale. And I'll make another video that will also give a little bit more intuition on there. That might seem very counterintuitive, but it's based on one way of thinking about it is thinking of an exponent as this. And this will also make sense if we start thinking of what 2 to the first power is. So let's go to this definition we just gave of the exponent.
We always start with a 1, and we multiply it by the 2 one time. So 2 is going to be we're only going to multiply it by the 2. I'll use this for multiplication. I'll use the dot. We're only going to multiply it by 2 one time. So 1 times 2, well, that's clearly just going to be equal to 2. And any number to the first power is just going to be equal to that number.
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