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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.

Mathematics
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\[x^{1/2}/(27x^6)^{1/3} = x^{1/2}/3x^{2} = 1/3 x^{1/2 - 2} \] I got \[1/3x^{-3/2} = 1/(3\sqrt{x^3})\]
Im will draw the equation
|dw:1333140979846:dw|

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Other answers:

yep 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))
yes
|dw:1333141131164:dw|
so then it is 1/3x?
No. 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.
index rule for division... subtract the powers x^{1/2} / 3 x^2 = 1/3 x^1/2 - 2} = 1/3 x^(-3/2)
what 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
That is the error pattern I saw. I say "error pattern" because it is a common error in Algebra.
oh so just leave it as the sqrt of x
|dw:1333141629395:dw| as campbell stated
What 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).
it says Use properties to simplify the expression. Answer should NOT include any negative exponents.
Oh I see your reasoning
@yrivers36 --> The instructions "sound" as if you were to do rational exponents but I am guessing. Usually the instructions are more explicit.
thats all that is there
Picking up from the answer in radicals, .. |dw:1333141957555:dw|
What 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).
checking now
it says follow the quotient rule for radical expressions. I found this in the book but the problem is on the lab
I 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.
Thank you so much
I 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.
ok i will do it that way
Okay, 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/roots-and-radicals/simplifying-radical-expressions.php

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