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. 9z^-1/2+2z^1/2

Accepted Answer

Welcome back. I am so glad you're here. We are. Given this expression 13. You raised to the negative 1/7 plus U. Raised to the 1/7. And we are essentially asked to factor here. So we're going to look at these two terms 13 U. Raised to the negative 1/7 and 15 U. Raised to the 1/7. And first we'll compare these coefficients these whole numbers here and say is there anything we can factor out? Do they have any common factors? No, 13 and 15 don't have any common factors. So we can't factor anything out there. Now we'll look at this U to the negative 1/7 and you to the positive 1/7. And we ask ourselves if there's anything we can factor out here and we'll yeah they're both use and they're both raised to a 1/7. Even the one is positive one is negative. But what do we factor out here? Well this is where we look for the common factor with the lowest power. So out of negative 1/7 and positive 1/7 which is the lower power. That's going to be the negative 1/7. So we are going to factor out. You raised to the negative 1/7. Or in other words we're dividing both of these terms by U. Raised to the negative 1/7. Oops that's not a one. So negative 1/7. Okay. So we figured out what we're factoring out now. We need to figure out what's left once we factored that out. So taking 13 U to the negative 1/7 divided by U to the negative 1/7. Well that 13 we couldn't factor anything out of that so we'll bring that down now. We'll take you to the negative 1/7 divided by U. To the negative 1/7. We recall from previous lessons that when we have two variables with exponents that are being divided we are going to subtract those exponents. So we're taking negative 1/7 minus negative 1/7. Which is the same as negative 1/7 plus 1/7. We have a common denominator so we can add our numerator negative one plus one is 0 0/7 which is zero. So we have you raised to the zero power. Anything raised to the zero power equals one. So we've got 13 times won 13 times one is 13. So we don't need to put 13 times one. We'll just keep it 13. All right now let's work on the second term 15 U. To the 1/7 divided by U. To the negative 1/7. So we couldn't factor anything out of the 15th. We'll bring down plus 15. And now again we are going to take you to the 1/7 divided by U. To the negative 1/7. And to do that we will subtract those exponents 1/7 minus negative 1/7 or 1/7 plus 1/7. And to do that we are going to add our numerator because we have a common denominator. One plus one is two. So this is to 7th, 2/7. So we've got you raised to the 2/7 or 15. You raised to the 2/7. Now we have factored this out now we can look at our answer choices. We've got you to the negative 1/7 times 13 plus 15. You to the 2/7 which matches with answer choice B. Well done, we'll catch you on the next one.

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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. 9z^-1/2+2z^1/2

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