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Math Help - Express each power as a radical.

  1. #1
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    Express each power as a radical.

    Hi guys,

    the task: Express each power as a radical.

    1. 9^1/2
    my anser:

    = root of 9

    2. m^-1/2
    my answer:

    = 1
    ------
    m^1/2

    = 1
    --------
    root of m

    3. 3k^2/5
    my answer:

    = 5 root of 3k^2

    4. ((pq^3)^4)^1/5
    my answer:

    = 5 root of pq^12

    5. x^2/3 y^1/4
    -------------
    x^1/2 y^1/2

    my answer:

    = x^4/6-3/6 y^1/4-2/4

    = x^1/6 y^-1/4

    Is that right? If not, please explain. Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Express each power as a radical.

    Quote Originally Posted by ford2008 View Post
    Hi guys,

    the task: Express each power as a radical.

    1. 9^1/2
    my anser:

    = root of 9

    2. m^-1/2
    my answer:

    = 1
    ------
    m^1/2

    = 1
    --------
    root of m

    3. 3k^2/5
    my answer:

    = 5 root of 3k^2

    4. ((pq^3)^4)^1/5
    my answer:

    = 5 root of pq^12

    5. x^2/3 y^1/4
    -------------
    x^1/2 y^1/2

    my answer:

    = x^4/6-3/6 y^1/4-2/4

    = x^1/6 y^-1/4

    Is that right? If not, please explain. Thanks.
    Your notation on 3 and 4 are possibly wrong.

    3. Is this 3k^{2/5} or (3k)^{2/5} If it is the second one then you are correct.

    4. Is this \left ( \left (pq^3 \right )^4 \right )^{1/5} or \left ( \left ( \left ( pq \right )^3 \right )^4 \right )^{1/5}

    The other ones look good.

    -Dan
    Thanks from ford2008
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  3. #3
    Junior Member
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    Re: Express each power as a radical.

    Hey Dan,

    thanks for your help.

    No. 3. is the first one, so then I am wrong. But what is wrong then in my answer?

    No. 4. is the first one. So is my answer right or not, if it is the first one?

    Thanks for your help.
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  4. #4
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    Re: Express each power as a radical.

    Quote Originally Posted by ford2008 View Post
    3. 3k^2/5
    my answer:

    = 5 root of 3k^2

    4. ((pq^3)^4)^1/5
    my answer:

    = 5 root of pq^12
    #3 .~~\sqrt[5]{3k^2} NOT 5\sqrt{3k^2}

    $4 .~~\sqrt[5]{p^4q^{12}}
    Thanks from ford2008
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  5. #5
    Super Member
    earboth's Avatar
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    Re: Express each power as a radical.

    Quote Originally Posted by ford2008 View Post
    Hi guys,

    the task: Express each power as a radical.

    ...
    3. 3k^2/5
    my answer:

    = 5 root of 3k^2

    4. ((pq^3)^4)^1/5
    my answer:

    = 5 root of pq^12

    ...
    Quote Originally Posted by ford2008 View Post
    ...

    No. 3. is the first one, so then I am wrong. But what is wrong then in my answer?

    No. 4. is the first one. So is my answer right or not, if it is the first one?

    Thanks for your help.
    According to your answer the 3 in your term doen't belong under the root-sign:

    3 \cdot k^{\frac25} = 3 \cdot \sqrt[5]{k^2}

     \left ( \left (pq^3 \right )^4 \right )^{1/5} = p^\frac45 \cdot q^{\frac{12}5}
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