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Math Help - Exponential, help me please

  1. #1
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    Exponential, help me please

    Okay so I've been doing alot of work with exponentials and now i've gone stuck on a leap from using simple exponents to using several.

    Here is what I could really need to have explained to me;

    (16x^6)^2/3

    So im thinking something like taking the third square of 16x^6, however I don't know if I can take the square out of something that has an exponential.
    I'd appreciate anyone sheding some light on this for me
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by Hanga View Post
    Okay so I've been doing alot of work with exponentials and now i've gone stuck on a leap from using simple exponents to using several.

    Here is what I could really need to have explained to me;

    (16x^6)^2/3

    So im thinking something like taking the third square of 16x^6, however I don't know if I can take the square out of something that has an exponential.
    I'd appreciate anyone sheding some light on this for me
    (16x^6)^{2/3}

    \left[(16x^6)^2\right]^{1/3}

    (256x^{12})^{1/3}

    256^{1/3}x^4

    \left[4^{4}\right]^{1/3}x^4

    4^{4/3}x^4

    4*4^{1/3}x^4

    4x^4 .^3\sqrt{4}
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  3. #3
    Junior Member teuthid's Avatar
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    Relevant Exponent laws

    There are two exponent laws that you need to employ:

    (xy)^p = (x^p)(y^P)
    (x^p)^q = x^(pq)

    These laws work for any real exponents (even if they're negative or fractions). I've attached a document that shows how these laws are applied in your particular example.

    Another key idea involved with this problem is that of fractional exponents' denominators representing roots. In your example, the 2/3 exponent is telling you to square the cubed root of the expression.
    Attached Files Attached Files
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  4. #4
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    Quote Originally Posted by teuthid View Post
    There are two exponent laws that you need to employ:

    (xy)^p = (x^p)(y^P)
    (x^p)^q = x^(pq)

    These laws work for any real exponents (even if they're negative or fractions). I've attached a document that shows how these laws are applied in your particular example.

    Another key idea involved with this problem is that of fractional exponents' denominators representing roots. In your example, the 2/3 exponent is telling you to square the cubed root of the expression.
    Whaw! Thanks alot
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