All right in this slide here, we're looking at positive numbers with a negative exponent right there. And number that is positive, but with a negative exponent, all we do is we take the reciprocal of that number. So for instance, five to the minus two power is actually one over five squared, or one over five to the to power, and we take the square of five, it's 25. So that's my answer. So five to the minus two power of fives minus squared is one over 25 Okay, the same thing with this one down here, we're up three to the minus two power. Well take the reciprocal of one over three squared, one over three squared is one over nine is my answer.
All right? If I want to find the decimal equivalent, I will use this example here. I tend to the minus two power is one over 10 squared, one over 10 squared is one over 100. And if I take down my calculator and do the reciprocal of 100, okay, it'll be zero dot 01 here and we'll do that let me let me stop this and we'll do this now. Okay, so here we go. So let's plug in 100.
And let's let's get my scientific because I think the reciprocal is there. No, it is not. Where is my reciprocal tool back to the standard. Ah, here we go. All right. So there we go.
It's right there. 1001 over x is my answer right there. All right, here's the reciprocal key. Okay. That's pretty easy. So let's go on to the next subject.
All right on this on this slide here, when a fraction is raised to a power, both the numerator and the denominator must be raised to that power. So we're going to show you some examples What I mean by that. So in this first example, here, we got two thirds cubed or to the third power. So basically, the only thing we do is we break this off right here, and we cube the numerator and we cube the denominator. And in this example, here, two times two times two times two is eight, and three times three times three is 27. So my answer is 827.
If you remember back, we talked about reducing a fraction. this fraction is in its simplest or lowest terms. So that's my answer right there. All right. Basically, we do the same thing if we are looking for the cube root of a fraction, in this example, here, eight over 27. Again, we're using this the same number.
All right? So basically, I look for the cube root of eight and the cube root of 27. And when I go through that manipulations, I find that it's two thirds right here. All right. So basically, we've gone through these we looked at the cube root, or how to find a cube root, I suggested to use a calculator. But when we have a fraction there, we just at that particular moment on both of these were you were dealing with that number as if it was one Same kind of manipulation, we just got to follow the rules.
All right. So what I've done here is I've given you two examples. I hit hit the pause button on this recording, and do the examples. And as always, when you continue, you'll see the answer on the next slide. All right. Okay, here are your answers.
Three over seven squared is 940 ninth, and that is in the lowest term. You can check me if you'd like, and then the, the square root of nine over 49 is, is three sevenths. And we're just going back the opposite. Alright, so again, if you have a problem with that, go through the presentation at the beginning, review some of the earlier slides and lectures where we spoke about finding the square and the square roots. Have number and come back and do this. And as always, as always, always always, okay, you have contact, you can contact me through this, this educational platform.
And you have a number if you look the number is, is if it's not on the slide, you'll see at the beginning and ending of every presentation that I give. Okay, we'll see you on the next slide now. Okay, like I promised, here are the answers four times two, all squared is 6416 times four. And I'm looking for the square root of that arm and the answer is eight here. All right, again, you know how to get ahold of me. Talk to you soon.
See in the next chapter.