Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathtard Group Title

Rewrite with rational exponents. Can someone please help me understand and work through this problem? \[\sqrt[6]{xy^5z}\]

  • 3 years ago
  • 3 years ago

  • This Question is Closed
  1. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok well do they want you to re-write it with fractional exponents? or ?

    • 3 years ago
  2. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It says re-write with rational exponents

    • 3 years ago
  3. simplephysics Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, well sqrt6 is like a power of 1/6. Let's see if we can apply that..

    • 3 years ago
  4. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sqrt[a]{x}=x^\frac{1}{a}\]

    • 3 years ago
  5. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok. So here's basically what you need to know to do all of these problems: \[\huge \sqrt[a]{b^kc^j} = b^{\frac{k}{a}}c^{\frac{j}{a}}\]

    • 3 years ago
  6. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sqrt[a]{b^kc^n}=(b^k c^n)^\frac{1}{a}=b^\frac{k}{a}c^\frac{n}{a}\]

    • 3 years ago
  7. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so how do I start so I take the b and move it over? make a the denominator and make k and j the numerators?

    • 3 years ago
  8. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The index of your radical what you will divide your powers by.

    • 3 years ago
  9. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    There's an 'is' missing from that sentence.

    • 3 years ago
  10. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I am still confused. I don't know where to begin. I feel like all of these problems are SOOO different

    • 3 years ago
  11. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    They are not. Remember the last problem you did? \[\sqrt[4]{(5a)^4} = (5a)^{\frac{4}{4}} = (5a)^1 = 5a\]

    • 3 years ago
  12. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It is easy to you because you understand I don't. I just don't learn that way. I need to see how it is solved. I have to actually be able to do the problem

    • 3 years ago
  13. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So in this case we have: \[\sqrt[6]{xy^5z}\] We can rewrite it as: \[\large (xy^5z)^{\frac{1}{6}}\]

    • 3 years ago
  14. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    And the recall that when you raise a power to a power you multiply the exponents.

    • 3 years ago
  15. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Raise a product to a power that is.

    • 3 years ago
  16. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You just divide each of the exponents by the index of the radical.

    • 3 years ago
  17. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What is the exponent on the x ?

    • 3 years ago
  18. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    1?

    • 3 years ago
  19. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Let's start at the beginning. Do you know how to write \[\sqrt{x}= x^{?}\]

    • 3 years ago
  20. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct. So now divide that 1 by 6 and the new exponent on the x will be 1/6

    • 3 years ago
  21. mathtard Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you.

    • 3 years ago
  22. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Now do the same thing for the y. The exponent on the y is 5, so 5 divided by 6 is 5/6

    • 3 years ago
  23. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Then again for the z and your result is: \[\large x^{\frac{1}{6}}y^{\frac{5}{6}}z^{\frac{1}{6}}\]

    • 3 years ago
  24. polpak Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    which doesn't seem 'simpler' at all. But that's sometimes how that goes.

    • 3 years ago
  25. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    another general example of applying law of exponent: \[(x^nyz^m)^{r}=(x^ny^1z^m)^r=x^{nr}y^{1r}z^{mr}=x^{nr}y^rz^{mr}\]

    • 3 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.