Factor and simplify each algebraic expression.

Question

16 x^{- \frac{3}{4}} + 32 x^{\frac{1}{4}}

Accepted Answer

Hi there. So this problem is that we want to perform Factory ization and simplify the given expression. 33 X two negative 16 plus 99 X. To the two thirds. So I'm gonna go ahead and rewrite this. So we have 33 X to the negative 1/6 Plus 99 x 2/3. No, The first step we want to check when we form factor Ization is really check are constants, so that is our 33 and are 99. Can we factor out the same number out of both of those contents constants is the question. And so I would say yes in this case we can And I think we can factor out 8:33. So a good check to see if we can factor out a number. Is I first like to see if we can take 99 Over 33 and see if that gives us a fact which it does. They'll give us three. So we will take out 33 out of both of those terms. 33 Times X 2 -1 Plus three X. to the 2/3. Now we will do the same for our exponents. This one's a little bit more tricky to tell if we can take out in a specific exponent. But what we can do is we can see what happens if we divide our exponents together. So if we look at our exponents, we have X to the 2/3 And we have X to the Native 1/6. So let's see if we can divide these, If we can we will take out X and -16 out of both terms. So we'll try and divide this expense. No, We have extra 2/3 on top extend native 16 on the bottom. When you divide exponents. If you recall from our book we're going to subtract the exponents if we have a division. So what I mean by that, So we have X to the two thirds. We will subtract our exponents which should be negative -16. No, we can't subtract these directly because our fractions have different denominators but we can say that X the two thirds. If we change the denominator to the six, that is actually going to be 4/6. Now we can go ahead and do our subtraction. And we actually, if you notice we have a minus a negative 1/6, that's going to change our sign the bus. And we have 1/6 that comes down which means this turns into X Power of 5/6. So we can divide those exponents, meaning that if we go back to our original factor we have 33 and we have X. Negative 1/6 Plus three X. The 2/3. We take out an X. And negative 16. We have 33 X to the negative 16. Now we factored out X- 916. When we do that we just get one by itself left and R three says there. Now we did the work over here. This is just X to the 5/6. Many of that. Our answer is answer A 33 X to the power of 1216 times one plus three X 56. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

Factor and simplify each algebraic expression. $16 x^{- \frac{3}{4}} + 32 x^{\frac{1}{4}}$

Key Concepts

Negative and Fractional Exponents

Factoring Algebraic Expressions

Simplifying Expressions with Like Terms

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