## yrivers36 Group Title 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 2 years ago

1. campbell_st Group Title

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

2. yrivers36 Group Title

Im will draw the equation

3. yrivers36 Group Title

|dw:1333140979846:dw|

4. campbell_st Group Title

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))

5. yrivers36 Group Title

yes

6. Directrix Group Title

|dw:1333141131164:dw|

7. yrivers36 Group Title

so then it is 1/3x?

8. Directrix Group Title

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.

9. campbell_st Group Title

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

10. yrivers36 Group Title

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

11. Directrix Group Title

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

12. yrivers36 Group Title

oh so just leave it as the sqrt of x

13. AsianDuck Group Title

|dw:1333141629395:dw| as campbell stated

14. Directrix Group Title

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).

15. yrivers36 Group Title

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

16. AsianDuck Group Title

17. Directrix Group Title

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

18. yrivers36 Group Title

thats all that is there

19. Directrix Group Title

20. Directrix Group Title

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).

21. yrivers36 Group Title

checking now

22. yrivers36 Group Title

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

23. Directrix Group Title

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.

24. yrivers36 Group Title

Thank you so much

25. Directrix Group Title

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.

26. yrivers36 Group Title

ok i will do it that way

27. Directrix Group Title

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