0:00 Hello my lovelies. It's Suzanna and today I want to show you how to solve problems like what is half of 2 to the^ of 22 or what is half of 4 to the^ of 22 or as a third problem. What is half of 10 to the^ of -12? Let's start with our first problem. What is half of 2 to the^ of 22? Usually when you want to find half of a number, let's say you want to find half of the number eight, then you just take the eight and divide it by two. So let's do exactly this here as well. Although our number looks a little bit more complicated, but we take the 2 to the^
0:47 of 22 and divide it by two to find half of this number. And now we only have to simplify this a little bit to find one of these answers. We have a power in the numerator and we can write this number here as a power as well. So we don't see an exponent here. But then we know that there is a one as our exponent. So we have a power divided by a power. the bases are the same, which is great because then there is a rule that tells us that we can just keep this base, the two, and then we just
1:35 subtract the exponents. We take the 22 minus this exponent down here minus the 1. So in total we have 2 to the^ of 22 - 1 = 21 which is result B. What is different here? If we want to find half of 4 to the^ of 22. Well first of all nothing changes. We just take this number and divide it by two as well to find half of this number. But this time we have base four here and here we have base two. So the bases are
2:23 not the same. But the good thing is that we can write the four in base 2. So we can write the four as 2 squared. This is the four and then we have to raise it to the power of 22. So we have to write this in parentheses and raise it to the power of 2. We just wrote the four as 2^ squared. So that we have base two here and we also have two in the denominator. If you want to write it as a power as well, we have 2 to the^ of one again. But here we have these parentheses. So it's not one power. We have a power
3:09 raised to another power. So I would like to apply a rule to get rid of these parentheses first and there is a rule that tells us that we just keep the base as it is and then we are allowed to multiply the exponents. So we have 2 * 22 which equals 44 and then in the denominator I have 2 to the^ of 1. Now we are in the same case again where our bases are the same. We now know oh nice we can keep the base and just subtract the exponents. 44 -1 = 43
3:54 which is answer D. And then in the last example everything is a little different. So let's see what do we have here. What is half of 10 to the^ of -12? Okay, first of all, we breathe. We take this number 10 to the power of -12 this time and divide it by 2 to find half of this beautiful number. What is the problem this time? This time we have base 10 here and here we still have base two. If we write it as 2 to the power of one again. But the problem is that we cannot write the 10 as 2 to
4:43 the power of something. We cannot write the 10 as 2 to the^ of three or four or whatever because the 10 is not a power of two. So we cannot get the same basis. Okay. What else can we do? um there is a possibility to do something with this expression here but I take different uh numbers to show you what I want to do. So let's say you have something like 3 to the^ of 5. Then this is a short version of saying I have three multiplied by three again by three by three again and by three again. So five times. Let's say I want to take one of these
5:30 threes out of this package. So I only want to have these four threes in a package. So I can write these as three to the^ of four. So I took one three out of this whole power. So I can write it as three times. This is my green three. And then I have a rest of 3 to the power of four. So instead of 3 to the^ of five, I can take one out of this power and then I don't have to the power of five anymore, but one less to the power of four. And I want to use this here. I want to take a
6:19 10 out of this package, out of this power. So I take one 10 out of there. And what is the rest? Well, we just saw that I have to decrease my exponent by one. Then I still have the same base, the 10, but I have to decrease the exponent. I have to subtract 1. -12 - 1 = -13. Then as my new exponent, I took 110 out of here. My two is still in the denominator and now I have a product
7:04 here. I am allowed to reduce this fraction. 10 / 2 = 5. So that in total I have 5 * 10 to the^ of -13. And this is answer D. If you like my video, please give it a thumbs up. That helps me a lot. I wish you a wonderful day and I hope to see you in one of my next videos.
