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Okay radical Tsc shmoop er's Here we go I got

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another question for you What value when cubed is equal

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to negative to sixteen times x to the fifth So

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how do we get there How do we get to

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the cube root of this thing Well we separate the

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factors under the cube so it looks like this We've

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got the cube root of negative to sixty next to

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the fifth which is the same as the cube root

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of negative one times cube root of to sixteen You

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should recognize that to sixteen Number because it's a special

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number We've got them the cube root of x to

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the fifth as its multiple can there So that's what

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It's gonna look like this Negative one to sixteen Fifty

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Yeah Now it's Time to find each of these three

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cube roots Slow and steady wins The race was going

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to come one at a time Here we go Cube

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root of negative one is negative one right Because negative

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one two The third powers Negative one All right Once

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that's done we'll turn our attention to the cube root

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of to sixteen Start by finding the prime factors of

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two sixteen there and so whole lot of threes And

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you know this because you could add two plus one

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plus six which gets you nine and that's evenly Divisible

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by three So you know three is going to be

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one of those factors right Well to do so we

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keep dividing out Smalls primes is possible Is shown here

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we got two Sixteen equals two times one Oh eh

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with vehicles two times two times fifty for which equals

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two times two times two two twenty seven which equals

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all this stuff right here at the end of the

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day It's two cubed times three cubed that's it Then

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we separate the factors and that allows us to take

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the cube roots here So cube root of to sixteen

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is the cube root of two to the third times

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three to the third which is same as the cube

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root of two to the third which is just too

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in the cube root of three to the third which

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is just three So the freakin answer is six You

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could have gotten there by knowing that six times six

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is thirty six I'm six is two Sixteen that's What

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we mean by it's one of those special numbers You'll

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see that a lot of tests So you may I

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just want to kind of note that in your brain

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All right well specifically then we go to take the

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cube root of x to the fifth by factoring out

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an x cube there that's the same as x to

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the three plus two which is same as x to

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the third times x to the squared or to the

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second power there orjust x squared So once again separate

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the factors under the cube root symbol Here we've got

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the cube root of exit third times x squared that

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gives us the cube root of x cubed times the

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cube root of x squared which equals x times the

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cube root of x squared right there So we found

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each of the three cube roots that we originally set

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out to find So it's time to finish the problem

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Put them all together and get your simplify on right

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so cube root of negative one time's cube root of

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to sixteen there times cube root of x fifth is

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the same as native One time six times acts times

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cube root of x squared which same as negative six

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x times the cube root of x squared wow that

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was ugly but were done And the answer is v 00:02:57.46 --> [endTime] and let's Just move on

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