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. 3m^2/3-4m^-1/3

Accepted Answer

Welcome back. I am so glad you're here. We are. Given this expression seven U. Raised to the 3/5 minus eight. You raised to the negative 2/5 and we are asked to essentially to factor this, we need to isolate the common factor with the lowest power. So we're going to compare these two terms. Seven U. Raised to the 3/5 and negative eight. You raised to the negative 2/5. And first we want to look at the whole numbers the coefficients here seven and negative eight. Is there anything that we could factor out of those two terms? No, there's nothing we could factor out. So now we're looking at you to the 3/5 and you to the negative 2/5. And is there anything we could factor out of those? Well, it might not be totally intuitive but there is this is where we are going to look for the factor with the lowest power. So between 3/5 and negative 2/5 which one is the lowest power? Well that would be negative 2/5. So that means we're going to factor out. You raised to the negative 2/5 and we're going to divide both of these terms by U. Raised to the negative 2/5. Well, we've figured out what we can factor out now, we need to figure out what's going to be left over. So let's start with the first time we've got that seven U. To the 3/5. Well we couldn't factor anything out of the seven. So we can bring the seven down. And now let's do you to the 3/5 divided by U. To the negative 2/5. 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 going to take 3/5 minus negative 2/5 or in other words 3/5 plus 2/5. We have a common denominator so we can add our numerator. So three plus two is five. So we've got 5/5 which equals one. So we've got you raised to the first which is you? All right? So we've got seven. You here. Now let's work on that negative eight. U. Raised to the negative 2/5. We can bring down the minus eight because we couldn't factor anything out of that. And now let's do the U. To the negative 2/5 divided by U. To the negative 2/5. Again we're going to take the exponents and subtract them. So negative 2/5 minus negative 2/5. Or in other words negative 2/5 plus 2/5. We have a common denominator so we can add our enumerators negative two plus two equals zero 0 50 or zero. So we have you raised to the zero power. Anything raised to the zero power equals one. So we've got a negative eight times one. Negative eight times one is negative eight. So we don't need to put that times one there. Alright we've done our factoring. We have an answer of you raised to the negative 2/ times seven U minus eight. We look at our answer choices in this matches with answer choice. D. Well done. We'll catch you on the next one.

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 3m^2/3-4m^-1/3

Key Concepts

Factoring

Exponents and Powers

Positive Real Numbers

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