simplify-each-expression-write-all-answers-with-only-positive-exponents-assume-that-all-variables-24

Question

Simplify each expression. Write all answers with only positive exponents. Assume that all variables represent positive real numbers.
$$
\frac{a^{4 / 3} \cdot b^{1 / 2}}{a^{2 / 3} \cdot b^{-3 / 2}}
$$

Amy Jiang · Accepted Answer

looks notice that we have, um, to a terms so we can use the quotient role between these two as well as these to be turns. Pelosi. Shall we have 18 power for a day and it&#x27;s minus. Do you have to? And then we have a beach of power 1/2 and that&#x27;s minus negative. Three. Over Tuesday, three plus do over to to have for over three minus 3/2. And that&#x27;s equal to negative, Um, 1/6. And then for 1/2 and two that&#x27;s equal to, um to That&#x27;s the right are a as a positive exponent, so that&#x27;s beach power to over 85 1/6.

Jason Williams · Answer

our task is to evaluate this expression with only positive exponents. All right, so our first thing we&#x27;re gonna do is you&#x27;re going to e that. Let&#x27;s see value the next one&#x27;s first, and we&#x27;re going to the valley with them inside the parentheses first. All right. So that means this age, the minus one to have to figure out what that becomes. All right, So you just have to remember that whenever we have a negative exponents, what that means is so a negative explode in my cage minus one that means is we&#x27;re going to do one divided by the number, eh? And then raise it to the positive of that exporter. So the positive and negative one is possible. It&#x27;s the one, all right. And then B squared remains the same. So that&#x27;s positive. All right. Okay. And we just have to remember now that whenever we have a new rated divided by a denominator, that is equivalent to multiplying by the reciprocal of the dog. All right, so be squared. Could be looked at as b squared, divided by one. All right. And so now we can convert this to a one of her, a multiplied by one over B squared the flip of the denominator. All right, the ministry. So this is equal to one over A B squared all of this to the minus three. All right. Now we can evaluate the mind. Reached the valley of the Native, exploded outside the parentheses. And so again, using the same logic, the negative three means we want one divided by whatever is in the prince&#x27;s easier. All right, so that is one over a three to the third. And then all of that. Oh, sir, a beaches. And then raise that to the positive of X on the positive of negative three is positive. Three. All right. And so when we do this multiplication out, we have one over one over baby squared. I was one over a b squared on over baby sweat. All right. And then So we multiply things of the same base of eight times, eight times a eight times eight times eight is going to give us won over eight to the third. And then similarly b squared times. The square time feast there is going to give us a beat to the sixth. All right? And so now we just remember again whenever we&#x27;re dividing, obliterated by denominated the same thing where we could treat that as a multiplication by the reciprocal. So we have one times the reciprocal of this. It&#x27;s the third beats, the sixth and so one times. That is just 8 to 36 and that is our answer.

Amy Jiang · Answer

Okay, so, Cyclops there by multiplying in our power of a negative three. So we get a to the power of negative one times negative three and B to the power of two times negative three. So does that give us? That&#x27;s a power of three over B to the power of negative six. So let&#x27;s rewrite this as a positive exponents. So we got one over breach of our six, and that&#x27;s equal to age of our three times breach of our six.

Joel Elford · Answer

this question asks us to simplify the expression. First thing we&#x27;re going to do is simplify what is in the bracket, and we&#x27;re going to, uh, a negative seven and the A squared. We&#x27;re gonna supply those and also the B turns. And since they have the same base under division, we subtract the exponents, so that will come out to the A to the negative seven minus two. Be the negative one minus negative. Four all to the 1/3 and well, then get a to the negative nine. Be too negative. Positive. Rather three and third and one of our exponents rules allows us to move what&#x27;s outside the bracket to every term inside the bracket, so that 1/3 will multiply to each to the A and the B. We&#x27;ll be left with a negative three and e to the one. Questions specifies that all exponents must be positive so we&#x27;ll do to get rid of the negative on the A. Is will take the reciprocal. We&#x27;ll be left with be over a

Amy Jiang · Answer

Okay, so let&#x27;s first notice that we have a term here as well as here. So let&#x27;s use our quotient rule between these two terms and then a zoo. Well, as between her to be terms. So we have h to the power of negative seven Might still, and beating power of negative one minus negative force. That&#x27;s plus for to the power of one of three. So that use mean 82 power of negative nine. And in beach, in power of three to the power of 1/3. I know we&#x27;ll bring in our power three. That&#x27;s a to depart. Negative. Nine times 1/3 and B to power of screen times 1/3. So that simplifies into eight of negative three on beach herb one. Okay, now rewriting this following term as a positive exponents, we get be over 80 Part three

Brandon Fox · Answer

Let&#x27;s start with the first princey, the four a square be cubed. And so let&#x27;s go ahead and power everything in there by that. Negative, too. So this is gonna be well, Actually, you know what? Let&#x27;s go ahead and move the negative. So they&#x27;re all positives so we can eat more easily. Do this. So let&#x27;s take the bottom down near the A Q. B moved to the top so that the negative fourth power turns to a positive four tower. And let&#x27;s move. Let&#x27;s do this. Let&#x27;s move the four a square, be cube to the bottom. So that is a ah positive to power. Now we can go ahead power everything in the princes by eso served, for example, before the the fourth power there on that first pregnancy, we can power the A cubed to that power for now, power to power. You multiply them so a to the 12th and then be to the first power. So one times four is de to the fourth and Ellis do the next princes on top. So, to to the third power is eight in a to the third powers a to the third power. Now that due to the negative one negative one Time Street is a B to the negative third power on the bottom Weaken square All these things as well four squared is 16 the A to the ah second power here due to attempts to is a to the fourth power and B to the third powerless multi three times to and you get be to the six power. Let&#x27;s start by multiplying the top two parentheses together. Now there&#x27;s not a number in this top one. We just can&#x27;t considered being a one here. So one times a is eight now a to the 12 power times a to the third power We add those powers together because we&#x27;re multiplying So a to the 15 power and the bees We also add their power so be in four plus Nega three is once will be the first power. This is over 16 either the fourth be the sixth. Now that we&#x27;re here, we can reduce the fraction by dividing both the top and bottom by eight so we can reduce this makes it a one If I that but it becomes in two now we don&#x27;t need the one on the top I will put the two on the bottom. We don&#x27;t need to write a one year if you don&#x27;t want Teoh right now anyway, um So what will get here is a to the 15th. Divided by eight of the fourth. We subtract their power. So a to the 11th. And then this be to the first power minus the 6116 is negative five. So be to the negative fifth power. Now that negative fifth power has to come to the bottom. Enjoying that, too, to become a positive power. So a the 11th over to be to the positive fifth power. This is our answer.

Problem

Simplify each expression. Write all answers with …

Problem 47 Hard Difficulty

Simplify each expression. Write all answers with only positive exponents. Assume that all variables represent positive real numbers.
$$
\frac{a^{4 / 3} \cdot b^{1 / 2}}{a^{2 / 3} \cdot b^{-3 / 2}}
$$

Answer

$a^{2 / 3} b^{2}$

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Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Finite Mathematics and Calculus with Applications

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Anna Marie V.

Caleb E.

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$a^{2 / 3} b^{2}$

Finite Mathematics and Calculus with Applications

Catherine R.

Anna Marie V.

Caleb E.

Joseph L.

Vectors Intro

Vector Basics - Example 1

Margaret L. Lial, Raymond N. Greenwell, Nathan P. RitcheyFinite Mathematics and Calculus with Applications

Catherine R.

Anna Marie V.

Caleb E.

Joseph L.

Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Finite Mathematics and Calculus with Applications