Potenzen multiplizieren - ganz einfach erklärt | Lehrerschmidt

Hello and welcome to Lever Schmidt. Today we are doing math together. We are in the calculation of powers and today we want to take a closer look at the area of ​​power multiplication. It's a little more detailed because there isn't just one type. several, so let's start now and first look at the area of ​​the same base. If you have the same base, then the following applies: iks raised to x iks hobi is ex raised to the power + b so you can see that the exponents can be added. if you have the same base, let's write merkel with the same base, the exponents or also called to the power of 2 can be added during multiplication ok, now let's take a closer look, the best way is always with two examples again. very briefly the lemma ex to the power of four to the power of 2 plus 5 and that's 47 and that's it.

It's that simple, that's the first part, now let's look at the second part. to what happens when we have the same exponent, then an exponent, I could also say raised to the power of the number, then raised to one raised to n, different bases but equal to the exponent, what do we do? then we make the parenthesis once b parenthesis too high in that means that the bases are multiplied in this case and the high number of the exponent remains the same write it down for us more with the same exponents the bases and in The multiplication of the dances multiply so it sounds strange we'll look at some examples again so quickly the mnemonic after high once b high n equals high good good tasks four to the power of three times three to the power of three ok war there are four times 3 and now to the power of three I can simplify that four times three is twelve so twelve to the power of three and then I finished one more task, of course what to use 10 to the power of six times three to the power of 6 like this and I can summarize that again 10 x 3 and the exponent is still 63 It's 30 to the power of 6 and I'm done, if you want to check everything, we'll say let's do that two to the power of three times two to the power of three, okay, that's 2 x 2, okay, two times two to the power of three and that's four to the power of three.

Well, now we want to check if that's actually true, so two to the power of three. it's 2 x 2 x 2 so eight times eight that's how you create it in your head that's 64 okay what does that look like with 4 x 4 x 44 x 4 16 times four is also 64 you can see so it works well so we have done this area and we reach the third part here there are frequent errors this time the same base and the same exponent so what we increase again is the same and now only once to the power of n but you have to see it many times something comes out bad ok good then remember if the base and the same exponent are the same the bases are multiplied and the exponent stays the same you don't see that it is difficult to calculate but let's take a look There is also an example, so just to briefly remember high because multiplied by n is high, everything is clear, so it's very simple two to the power of two times two to the power of two until then nothing more than two times two to the power of 22 x 24 then four to the power of two is clearly fine one more thing 7 to the power of three times seven to the power of three is then seven times seven to the power of three so 49 to the power of three one last thing, but I think it's already clear 3 squared times three squared is then three times three square brackets three times three is nine nine squared so you can check that briefly, let's make 3 squared is three times three so 99 x 9 is 81 and nine squared is also nine times nine, so it's also 80, so we don't even need a calculator, then we have it.

In the end we will summarize everything again in an overview like this. Multiply powers so that once you have the same base like this and if the base is the same, then xa x iks to the power of b is iks to the power + b a quick example three squared times three to the power three is then three raised to the power of 2 +3 and which in turn is three raised to the power of ok, we quickly underlined that then we looked at it b is equal to the exponent of the fraction number of the rudder we said yes to the power once to the power of an and then we find that also and finally c the combination of the same base and the same exponent and that is where I got said book once raised to the power because there is nothing more than high an example task two to the power of three times two to the power of three is two two to the power of 3, then four to the power of three and then we're done.

Now you have seen all the possible areas of multiplying powers in one video and that. Do you have to learn this page and maybe even take a screenshot, women? You have to keep that in your head. It is 100% important when you are working. There are always these tasks of different variations. The good thing is that when you multiply them by powers, I understood that it is the same when dividing, but pay attention, adding. and subtraction are different, of course I also have videos, okay, that's all.