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Math Help - How are these two equivalent?

  1. #1
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    How are these two equivalent?

    Show that  \frac{2^\frac{2}{3}}{4}=\sqrt[3]{\frac{1}{16}}.


    Any help showing detailed working out would be appreciated!
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  2. #2
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    Work with this.
    \sqrt[3]{{\frac{1}<br />
{{16}}}} = 2^{-\frac{{ 4}}<br />
{3}}
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  3. #3
    Super Member Quacky's Avatar
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    Start by writing everything as a power of 2

    \frac{2^\frac{2}{3}}{4}=\sqrt[3]{\frac{1}{16}}

    \displaystyle\frac{2^\frac{2}{3}}{4}

    =\displaystyle\frac{2^\frac{2}{3}}{2^2}

    =\displaystyle(2^\frac{2}{3})(2^{-2})

    Using the law of indices, (x^a)(x^b)=(x^{a+b})

    Apply that here, then tidy up to give you the answer you seek.

    Edit: Unfortunately, I am far slower than Plato, as usual. =.=
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  4. #4
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    Quote Originally Posted by Plato View Post
    Work with this.
     2^{-\frac{{ 4}}<br />
{3}}
    Wait a minute. How did you get  2^{-\frac{{ 4}}<br />
{3}} ?
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  5. #5
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    Quote Originally Posted by Joker37 View Post
    Wait a minute. How did you get  2^{-\frac{{ 4}}<br />
{3}} ?
    I understand the way exponents work.
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