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. -4a^-2/5+16a^-7/5

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression seven U. Raised to the negative 2/7 minus 35. You raised to the negative 9/7. And we are essentially going to factor this. So we've got two terms here, you've got the seven. You race to the negative 2/7 and this negative 35. You race to the negative 9/7. We're going to compare the comparable parts. So the whole numbers here, the seven and the negative 35. And we're going to ask ourselves what is a common factor that we can factor out with those two numbers. So between seven and negative 35 those are both divisible by seven. So we can factor out a seven from those two. Now we're going to look at these use and we've got you to the negative 2/7 and we've got you To the -9/7. And here is where we are going to isolate the common factor with the lowest power. So when we've got two variables with exponents, we're going to look for the one with the lowest power. And in this case comparing negative 2/7 and negative 9/7. The one that's closer to negative infinity. The lower power is negative 9/7. So we are going to divide both of these by U. Raised to the negative 9/7. Or in other words we're factoring out a U. Raised to the negative 9/7. So now that we've factored out the common factor with the lowest power. Now we need to figure out what's left on the inside. So let's figure out from that first term. First dividing seven U. To the negative 2/7 by seven U. To the negative 9/7. We'll start with seven divided by 77 divided by seven is one. And for you raised to the negative 2/7 divided by U. Raised to the negative 9/7. When we have two variables that are that have exponents and they're being divided we are going to subtract the exponents as we recall from previous lessons. So we'll take negative 2/7 minus negative 9/7 or in other words we have negative 2/7 plus 9/7. We have a common denominator so we can add the numerator negative two plus nine is seven. So this is 7/7 which is one. So this is you to the first or just you. And so we've got one times you hear well one times U. Is just you. So I'm going to write you. Alright that's the first term factored out. Now let's work on the negative 35. You to the 9/7 we'll start with the whole number negative 35 divided by seven is negative five. And you raised to the negative 9/7 divided by U raised to the negative 9/7. Well again we are going to subtract our exponents. So negative 9/7 minus negative 9/7 or in other words negative 9/7 plus 9/7. Got it common denominators. So let's add our numerator negative nine plus nine is zero. So 07 which is zero. We've got you to the zero. Well anything raised to the zero power equals one. So we've got negative five times one negative five times one is just negative five so we can leave it as negative five. So we've got this factored we've got seven U. Raised to the negative 9/7 times U minus five. We look at our answer choices and this 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. -4a^-2/5+16a^-7/5

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