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Math Help - Solve for X

  1. #1
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    Solve for X

    Help, Solve for X
    4x^-2/3 = 16

    i got to the point where 1/3\sqrt{4x^2} = 16 , then i am totally lost

    Also what is the rule for a base with a power of negative fraction? Why do you have to flip ex: x^-1/2. 1/\sqrt{x}

    Thank You

    PS: am i posting in the corrct subforum?。。.
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  2. #2
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    I believe this is the correct sub forum

    Can you please confirm the problem?

    4x^{-2/3} = 16

    or

     (4x)^{-2/3} = 16
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  3. #3
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    Quote Originally Posted by pickslides View Post
    I believe this is the correct sub forum

    Can you please confirm the problem?

    4x^{-2/3} = 16

    or

     (4x)^{-2/3} = 16
    It is the top one 4x^{-2/3} = 16 , but do you mind demonstrating the bottom one also? ty
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  4. #4
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    Use the properties of exponentiation.

    solving both ways...

    <br />
(4x)^{-2/3} = 16<br />

    <br />
(4x) = 16^{-3/2}<br />

    <br />
x = (16^{-3/2})/4<br />

    or in your case

    <br />
4x^{-2/3} = 16<br />

    <br />
x = (16/4)^{-3/2}<br />
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  5. #5
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    Quote Originally Posted by Billyboy View Post
    Use the properties of exponentiation.

    solving both ways...

    <br />
(4x)^{-2/3} = 16<br />

    <br />
(4x) = 16^{-3/2}<br />

    <br />
x = (16^{-3/2})/4<br />

    or in your case

    <br />
4x^{-2/3} = 16<br />

    <br />
x = (16/4)^{-3/2}<br />
    Thank You Billy, the answer key for 4x^{-2/3} = 16 is 1/8, how do you simplify it into 1/8?.. i am having big problems with negative fraction powers
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  6. #6
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    <br />
x = (16/4)^{-3/2}<br />

    <br />
x = 4^{-3/2}<br />


    raising a nonzero number to a "−" power produces its reciprocal...

    <br />
x^{-1} = 1/x<br />

    and

    <br />
x^{-2}=1/x^2<br />

    i.e.

    <br />
x^{-a}=1/x^a<br />

    think you get the idea...

    ...taking what you know from above and understanding that the numerator raises the number to that power (in this case ^3) and the denominator takes the root (in this case 2nd root or sqrt) therefore you can simplify...

    ...This

    <br />
x = 4^{-3/2}<br />

    is the same as this...

    <br />
x = 1/(4^{3/2})<br />

    is the same as this...

    <br />
x = 1/sqrt(4^3)<br />

    Therefore, we easily solve...

    <br />
4^3 = 64<br />

    and

    <br />
sqrt(64) = 8<br />

    Thus you get...

    <br />
x = 1/8<br />
    Last edited by Billyboy; November 18th 2009 at 11:27 PM.
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  7. #7
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    a good property to know...

    <br />
(a/b)^{-1} = b/a<br />



    Also, take for example:

    <br />
x^{a}=y<br />

    to solve for x...

    <br />
x^{a(a^{-1})}=y^{(a^{-1})}<br />

    <br />
(a*a^{-1} = a * 1/a = 1)<br />

    sooo...

    <br />
x = y^{1/a}<br />
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