Use the quotient rule to simplify the expressions in Exercises 23...

Question

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x

Accepted Answer

Welcome back. I'm so glad you're here. We have this expression, we have the square root of 108 of the fifth divided by the square root of 48 of the third. And we are to simplify this using the quotient rule. What is the quotient rule? We recall from previous lessons that when we have the square root of a divided by B, that is the same as the square root of a, divided by the square root of B. And because these two things are equivalent, we can work from the right side of the equation to the left as well, which is what we have here. We have a square root divided by a square root. So we can now rewrite this as taking the square root of the two things that are being divided. So we have the square root of 100 A. To the fifth divided by four A. To the third. Now we can go ahead and do that division that's occurring. So this is the square root of well 100 divided by four is 25 A to the fifth in the numerator and A to the third in the denominator. And we recall from previous lessons that when we're dividing two variables that are the same variable and they have exponents. We are going to subtract those exponents. So now we'll have the square root of 25 A. To the fifth divided by A to the third. We take five minus three leaves us with a to the second or a squared And we can take the square root of 25 and the squared of a square. The square of 25 is five. The square root of a squared is a. We look at our answer choices and that matches with answer choice. A well done will catch on the next one.

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