Problem

Simplify: $\left(\frac{5}{4}\right)^{-3}$.

Problem 5 Easy Difficulty

Simplify: $\left(z^{5}\right)^{-2}$.

Answer

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Elementary Algebra

Chapter 7

Factoring

Section 1

Negative Exponents

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Video Transcript

So when we're doing this, we're gonna have to simplify both of these by doing a long division. So I'm going to set it up right now. But for all the values we don't have, like, see to the fourth and see to third and just a Z one, we're gonna put zero as our police holder. And we'll come in handy when we're working through the problem. And now this is gonna be divided by Z minus two. Okay, so first we're trying to get rid of this value saw remained really zero. So we're gonna multiply by sea to do it fourth. So when he multiplied this in this, you get see to the fifth minus two Z to the fort. So again, we're subtracting these. We're doing this so we get nothing here. But then you get a to Z to the fort positive, and they get plus zero z to the third minus three z second plus zero Z minus 20. Now we're looking at this value. So here we're going to multiply by not to play the Z minus two polynomial by two Z to these to the third. So just go here to this So that leaves us with down here to Z to the fourth minus four Z to the third. And so when you subtract thes again, we're not gonna have any value here. But we're gonna have four to see to the third here, minus three z to the second plus zero z minus 20. All right, now we have this one right here, and we're gonna multiply by plus for Z to the second to this to this, um, top. Get rid of that. Values were going to get four z to the third, um, minus eight z second power. And again, we're gonna subtract this so this again crosses out. And here we're gonna have five Z to the second plus zero z minus 20. Now we have come Now we're trying to get rid of this. So here we're going to multiply by plus five z. So that's going to give us this to this. And then when we get the value, we're gonna put it down. Here is we give five Z squared minus 10 z. So when we subtract thes again, this crosses out and we get tensy minus 20 years. So I'm going to move the rest of the work up here. So again, we have 10 Z minus 20 here. And now to get rid of this whole thing, we're going to multiply by plus tons. So we're going to multiply this value to this and that gives us 10 Z minus 20. So that's perfect. So if we subtracted, will get a final remainder of zero, which gives us our answer, which is up here on the top of this polling Long division problems. I'm gonna re ready. Here. We get seats before it plus two z to the third plus four z to the second plus five z two plus five C plus 10. So this is the final answer.

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Elementary Algebra

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Problem

Simplify: $\left(\frac{5}{4}\right)^{-3}$.

Problem 5 Easy Difficulty

Simplify: $\left(z^{5}\right)^{-2}$.

Answer

Related Courses

Elementary Algebra

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Discussion

Top Educators

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Watch More Solved Questions in Chapter 7

Video Transcript

David Arnold

Elementary Algebra

Elementary Algebra

David ArnoldElementary Algebra

David Arnold

Elementary Algebra