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Math Help - Radical Multiplication

  1. #1
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    Radical Multiplication

    See attachment for math question.
    I have to multiply and then simplify.
    Attached Thumbnails Attached Thumbnails Radical Multiplication-radical-multiplication.jpg  
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  2. #2
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    Quote Originally Posted by sologuitar View Post
    See attachment for math question.
    I have to multiply and then simplify.
    \sqrt{2^{109}} \cdot \sqrt{x^{306}} \cdot \sqrt{x^{11}} = 2^{\frac{109}2} \cdot x^{\frac{306}2} \cdot x^{\frac{11}2}

    Use the law of powers:

    a^x \cdot a^y = a^{x+y}

    Btw: 2^{\frac{109}2} = 2^{54+\frac12}
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  3. #3
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    I got...

    Quote Originally Posted by earboth View Post
    \sqrt{2^{109}} \cdot \sqrt{x^{306}} \cdot \sqrt{x^{11}} = 2^{\frac{109}2} \cdot x^{\frac{306}2} \cdot x^{\frac{11}2}

    Use the law of powers:

    a^x \cdot a^y = a^{x+y}

    Btw: 2^{\frac{109}2} = 2^{54+\frac12}
    I got [2^(109/2)] [(x^(317/2)]

    Base 2 and base x are not the same and so, we cannot apply the rule
    a^x * a^y.

    Correct?
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