Factor out the least power of the variable or variable expression...

Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 6y^3(4y-1)^-3/7-8y^2(4y-1)^4/7+16y(4y-1)^11/7

Accepted Answer

Right? The given expression of isolating the common factor with the lowest power. Now we're going to do this by taking out the lowest power of everyone in these terms. We notice here, our lowest power is three k minus two to the negative 2/5. So we'll take out three k minus two, negative 2/5. That leaves us with 10K. It's the third here. Now, I'm gonna take out this ***, 2/5 away from this to the 3/5 we're taking out exponents, we're gonna subtract the two exponents from each other. So we have 3/5 minus negative 2/5. That corresponds with three k minus two. It's the 5/5 which we can write this just as that to the first re file will just be one. Well go on 25 k Times three K -2. Same thing here. Eight minus 8/5 minus negative 2/5. That gives us 10/5, which we know to number five is just equal to two. So that will be a squared. We just want to take out anything else in common. We have. We notice here we have a ks uncommon in every one of these terms. Let's take out one K out of all of these K, three k minus 22 negative 2/5. Then we have 10-K 2. The second -15 k times three K -2 Plus 25 times three K -2 Squared. We'll take out one more thing, which is a factor of five. Each. One of these have a common factor of five. So we take out the five from everything we have five K. Three K minus 2 to 92 5th take it five out of 10. We get to k squared -3 K. here three K -2 Plus five times 3 K -2 Squared. Now we want to simplify everything in the parentheses. So we have five K three k minus 22 negative 2/ inside we have two k squared minus nine K squared. Wanted to ship you plus six K plus five times nine K squared minus 12 K plus four. Which is the expansion of our three k minus two squared go even further five K three k minus two negative 2/ two K squared minus nine K squared will say negative seven K squared plus six K. Then we have plus 45 k squared minus K plus 20 Simplifying even further it's 5K three K -2. It's a negative 2/5 38 case win -54 came finally plus 20. Finally we can take a two out of every term in this parentheses. Take the two out. That too. Will multiply the five. We get 10-K 3 k minus 22 negative 2/ times 19 K squared -27 K plus 10. Now we can't simplify this any farther. That makes the answer to our problem answer. D. Okay I hope to help you solve the problem. Thank you for watching. Goodbye.

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Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 6y^3(4y-1)^-3/7-8y^2(4y-1)^4/7+16y(4y-1)^11/7