Results 1 to 13 of 13

Math Help - Simplifying exponential expressions

  1. #1
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52

    Simplifying exponential expressions


    Simplifying exponential expressions, can you please confirm my solutions are correct?

    A.

    (3x^4y^5z^7)^5 / (-3x^3yz^4)^7

    = -1^5-7x^20-21y^18z^7 = -1^-2x^-1y^18z^7

    Solution I arrived at:

    y^18z^7/ x

    B.

    [x^(a+b)]^(a-b) / [x^(a-2b)]^(a+2b)

    Solution:
    = 1^(3b^2)

    Thanks in advance.

    Sincerely,

    Raymond MacNeil
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Just to be clear, the original expressions are:

    A.

    \frac{(3x^{4}y^{5}z^{7})^{5}}{(-3x^{3}yz^{4})^{7}}, and

    B.

    \frac{[x^{a+b}]^{a-b}}{[x^{a-2b}]^{a+2b}}.

    Is that right?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52
    That's correct sir. I tried importing images from Microsoft Equation editor but they didn't seem to want to upload.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Fantastic. The most important two concepts you need to solve this problem are the following:

    1. (a^{b})^{c}=a^{bc}, and

    2. \frac{1}{a^{b}}=a^{-b}.

    I would probably apply # 1 first. What does that give you?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52
    for the First one I have now arrived at the solution: -y^18z^7/9x

    Is that correct? I'll work on the second one again.
    Last edited by raymac62; May 14th 2011 at 03:46 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I would agree with your answer, since I know what you meant to write. However, you should technically write -(y^18)(z^7)/(9x) to be completely unambiguous. Don't write so that people can understand you: write so they can't misunderstand you!
    Last edited by Ackbeet; May 16th 2011 at 12:58 AM. Reason: Mis-spelling.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445
    Your solution to the second is incorrect.

    \displaystyle \begin{align*}\frac{\left(x^{a + b}\right)^{a - b}}{\left(x^{a-2b}\right)^{a+2b}} &= \frac{x^{(a + b)(a - b)}}{x^{(a + 2b)(a - 2b)}}\\ &= \frac{x^{a^2 - b^2}}{x^{a^2 - 4b^2}} \end{align*}.

    Can you go from here?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52
    I guess I get baffled here because I am not entirely sure what to do when you have positive and negative exponents. Do you turn it into a complex fraction? I substituted numbers for the the unknowns and it seems to work out that the correct solution would be x^(3b^2). I acknowledge previously I had a "1" instead of maintaining the variable "x". Though perhaps I am still doing something wrong. Do you mind showing me the entire process because I have never encountered this type of expression before and the course has not supplied any examples demonstrating how to carry this out either.

    Thanks in advance.

    Sincerely,

    Raymond.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445
    x^(3b) is correct.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52
    Quote Originally Posted by Prove It View Post
    x^(3b) is correct.
    So the answer is not x^(3b^2)?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    ProveIt had a typo, or maybe a thought-o in post # 9. The correct answer is

    x^{3b^{2}}.
    Last edited by Ackbeet; May 16th 2011 at 08:16 AM. Reason: Poster removed ambiguity.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52
    Thanks, yeah I edited right after once I realized the ambiguity. Thanks for confirming.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplifying Expressions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 21st 2011, 05:30 PM
  2. Simplifying Expressions
    Posted in the Pre-Calculus Forum
    Replies: 18
    Last Post: September 28th 2010, 03:29 AM
  3. simplifying expressions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 9th 2008, 08:45 PM
  4. Simplifying Expressions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 6th 2008, 05:23 PM
  5. simplifying expressions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 29th 2008, 10:28 AM

Search Tags


/mathhelpforum @mathhelpforum