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 2 years ago
Just want to check to make sure answer is correct. Simplify the expression.
sqrt of x divided by cubed rt of (27x^6). The answer that I got was 1/3x. Please explain.
 2 years ago
Just want to check to make sure answer is correct. Simplify the expression. sqrt of x divided by cubed rt of (27x^6). The answer that I got was 1/3x. Please explain.

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campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.1\[x^{1/2}/(27x^6)^{1/3} = x^{1/2}/3x^{2} = 1/3 x^{1/2  2} \] I got \[1/3x^{3/2} = 1/(3\sqrt{x^3})\]

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0Im will draw the equation

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1333140979846:dw

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.1yep my answer still holds... in the denominator (27x^6)^1/3 = 3x^2 so x^(1/2)/3x^2 = 1/3 x(1/2  2) = 1/3 ( x(3/2))

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1333141131164:dw

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1No. Square root of x and then just x are not the same so they do not divide out. Think of square root of 4 and then just 4. They do not divide to 1.

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.1index rule for division... subtract the powers x^{1/2} / 3 x^2 = 1/3 x^1/2  2} = 1/3 x^(3/2)

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0what I think I was doing was taking the sqrt of x which I think = x and then canceling out one the x on the numerator and one x from denomenator

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1That is the error pattern I saw. I say "error pattern" because it is a common error in Algebra.

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0oh so just leave it as the sqrt of x

AsianDuck
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1333141629395:dw as campbell stated

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1What are the instructions for the problem? If you were doing rational exponents, then I would not leave it as sqrt of x. By rational exponents, I mean something like x^(1/2).

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0it says Use properties to simplify the expression. Answer should NOT include any negative exponents.

AsianDuck
 2 years ago
Best ResponseYou've already chosen the best response.0Oh I see your reasoning

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1@yrivers36 > The instructions "sound" as if you were to do rational exponents but I am guessing. Usually the instructions are more explicit.

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0thats all that is there

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Picking up from the answer in radicals, .. dw:1333141957555:dw

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1What sort of properties are in the book to which the instructions "Use *properties* to simplify the expression." Were any of the properties for rational exponents. If so, you'll see a property such as the following: x^a / x^b = x^ (a  b).

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0it says follow the quotient rule for radical expressions. I found this in the book but the problem is on the lab

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1I think I would leave the answer as sqrt of x over the quantity (3x^2) but consider showing on the side of the paper the continuation to rational exponents. Just a second, and I'll check the quotient rule for radical expressions. Also, I'll upload some properties of rational exponents for you to view.

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1I have decided that based on this, if I were doing the problem for class, I would leave the radical in the answer and stop there.

yrivers36
 2 years ago
Best ResponseYou've already chosen the best response.0ok i will do it that way

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, and here's the link for the Quotient Rule. The section I uploaded was truncated. In case you want to practice on other problems, you can go to the source: http://www.mathportal.org/algebra/rootsandradicals/simplifyingradicalexpressions.php
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