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Math Help - Simplifying using Rational Exponents

  1. #1
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    Simplifying using Rational Exponents

    Hi everyone!

    I have a question on this one problem regarding rational exponents. Here is it:

    Simplifying using Rational Exponents-fireshot-screen-capture-693-myalgebra-solve-your-algebra-problems-online-myalgebra_com_.png

    I got this far:

    Simplifying using Rational Exponents-problem-02.png

    I'm a little frustrated now because I don't know what the next step is. I would appreciate any help.

    Thank you so much, I really appreciate it!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Simplifying using Rational Exponents

    If it were me, I would work first within the parentheses using:

    \sqrt[n]{x^m}=x^{\frac{m}{n}}

    Next, use the rule for exponents:

    a^b\cdot a^c=a^{b+c}

    Then finally use the rule for exponents:

    \left(a^b \right)^c=a^{bc}
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  3. #3
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    Re: Simplifying using Rational Exponents

    Quote Originally Posted by choti96 View Post
    Click image for larger version. 

Name:	FireShot Screen Capture #693 - 'MyAlgebra - Solve Your Algebra Problems Online' - myalgebra_com_.png 
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    I got this far:
    Click image for larger version. 

Name:	problem 02.png 
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    Convert these to fractional exponents and combine.
    \sqrt[3]{7} = 7^{\frac{1}{3}} \;\& \,\sqrt[4]{7} = 7^{\frac{1}{4}}

    You simply use the laws of exponents .
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  4. #4
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    Re: Simplifying using Rational Exponents

    Thank you so much, Plato! You are incredible!
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  5. #5
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    Re: Simplifying using Rational Exponents

    Thanks for the help, Mark!
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