- yrivers36

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.

- jamiebookeater

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- campbell_st

\[x^{1/2}/(27x^6)^{1/3} = x^{1/2}/3x^{2} = 1/3 x^{1/2 - 2} \]
I got \[1/3x^{-3/2} = 1/(3\sqrt{x^3})\]

- yrivers36

Im will draw the equation

- yrivers36

|dw:1333140979846:dw|

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- campbell_st

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))

- yrivers36

yes

- Directrix

|dw:1333141131164:dw|

- yrivers36

so then it is 1/3x?

- Directrix

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.

- campbell_st

index rule for division... subtract the powers
x^{1/2} / 3 x^2 = 1/3 x^1/2 - 2} = 1/3 x^(-3/2)

- yrivers36

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

- Directrix

That is the error pattern I saw. I say "error pattern" because it is a common error in Algebra.

- yrivers36

oh so just leave it as the sqrt of x

- anonymous

|dw:1333141629395:dw| as campbell stated

- Directrix

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).

- yrivers36

it says Use properties to simplify the expression. Answer should NOT include any negative exponents.

- anonymous

Oh I see your reasoning

- Directrix

@yrivers36 --> The instructions "sound" as if you were to do rational exponents but I am guessing. Usually the instructions are more explicit.

- yrivers36

thats all that is there

- Directrix

Picking up from the answer in radicals, ..
|dw:1333141957555:dw|

- Directrix

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).

- yrivers36

checking now

- yrivers36

it says follow the quotient rule for radical expressions. I found this in the book but the problem is on the lab

- Directrix

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.

##### 1 Attachment

- yrivers36

Thank you so much

- Directrix

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.

##### 1 Attachment

- yrivers36

ok i will do it that way

- Directrix

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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