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. 6r^-2/3-5r^-5/3

Accepted Answer

Welcome back. I am so glad you're here we are. Given this expression 11. You raised to the negative 3/16 minus 12 U raised to the negative 19 16th and were asked to isolate the common factor with the lowest power. So essentially we're factoring here we have two terms and we're going to compare the comparable parts for each term. So in other words let's look at the whole numbers here we've got 11 and negative 12. Is there anything that we can factor out of 11 and negative 12? No they don't have any common factors. How about you? Race to the negative 3/16 and you race to the negative 19 16th? Well intuitively they don't exactly have a common factor but we actually can factor something out. This is where we look for the lowest power. So we're going to be comparing you raised to the negative 3/16 and you raised to the negative 19 16th which of those has the lower power. Which power between negative 3/16 and negative 19 16th is closer to negative infinity. And in this case that's going to be negative 19 16th. So we're going to factor out a U. Raised to the negative 19 16th. Or in other words we're dividing both of these numbers by while both of these variables by U raised to the negative 19 16th. So that's what we are factoring out. Well once we've factored that out we still need to see what's left over. So we need to divide both of those you variables. We can bring down the 11 cans Since we couldn't factor anything out of the 11. But how about you raised to the negative 3/16 divided by U raised to the negative 19 16th. We recall from previous lessons that when we have variables that are being divided and they have exponents we are going to subtract those exponents. So we will be taking negative 3/16 minus negative 19 16th. Or in other words negative 3/16 plus 16th. We have a common denominator so we can add our numerator negative three plus 19 equals 16. So 16 16th which equals one. So we've got you raised to the first power which is just you. So we've got 11. You left here are right. How about this second term? This negative 12 you raised to the negative 19 16th. So we can bring down our minus 12. We can't factor anything out of that. And now let's do the division for you raised to the negative 1916 divided by U. Raised to the negative 19 16th. Again we are going to subtract these exponents and negative 1916 minus negative 16th is the same as negative 19 16th plus 19 16th. We have a common denominator so we can add our numerator negative 19 plus 19 is zero. So 0/16 which is zero or in other words we have you raised to the zero power. Well anything raised to the zero power is equal to one. So we've got negative 12 times one here. Well negative 12 times one is negative 12. So we don't need to put that times one there. And now we've got this factor. So we look at our answer choices and we're looking for you raised to the negative 16th Times 11 U. -12. And that 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. 6r^-2/3-5r^-5/3

Key Concepts

Factoring

Exponents and Powers

Least Power of a Variable

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