Define power of ten5/1/2023 ![]() ![]() When we go from nine to three, divide by three, so based We divided by three, and that makes sense,īecause we're multiplying by one less three, so we divide by three to go from 81 to 27, weĭivide by three again if our exponent goes down by one, and we divide by three again What happened to the value? Well, going from 81 to 27, ![]() ![]() Do you notice a pattern every time we decrease the exponent here by one? We want three to the fourth, and now we go three to the third. If I said three to the third power, that's three times three The fourth power, that's three times three times three times three which is going to be equal to 81, and let me just write down that this is going to be equal to 81. Let's say we have three and I could say three to So does this make sense that two to the zero power is equal to one? Well, let's think about it another way, and let's do a different base. We're not gonna multiply it by any two, so we're just With a one and you multiply it by the base zero times, so Well, the way we just talkedĪbout it, we just said exponentiation is you start If you were the mathematics community, how would you define two to the zero power so it is consistent withĮverything that we just saw. Of what an exponent is, what would two to the zeroth power be? I encourage you to just thinkĪbout that a little bit. Now let's ask ourselfĪn interesting question. What would two to the first power be? Well, that would be one, and we would multiply it by one two, one times two, which, of course, is equal to two. This definition I just did, what would two to the second power be? Well, this would be one times two twice, so one times two times two, which, of course, would be equal to four. Go with this definition right over here, and this, of course, is going to be equal to eight. Multiplying it by two three times, so actually, let's just Say this is the same thing as taking a one and then So two times two times two, or equivalently, we could Like two to the third power, we could view this as taking three twos and multiplying them together, ![]()
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