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Math Help - Express radicals in exponential form.

  1. #1
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    Express radicals in exponential form.

    Hi guys,

    the task: Express each radical in exponential form. Simplify using the exponent laws when possible.

    1. root of k^2/3
    my answer:

    = (k^2/3)^1/2

    = and then?

    2. root of ab^2
    my answer:

    = (a)^1/2 (b^2)^1/2

    = a^1/2 b^1

    3. 4 root of 81 x^8 y^12
    my answer:

    = (81)^1/4 (x^8)^1/4 (y^12)^1/4

    = 81^1/4 x^2 y^3

    4. cube root of x and square root of x
    my answer:

    = (x)^1/3 (x)^1/2

    = x^2/6+3/6

    = x^5/6

    Is that right or not? Explain please. Thanks.
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  2. #2
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    Re: Express radicals in exponential form.

    Quote Originally Posted by ford2008 View Post
    the task: Express each radical in exponential form. Simplify using the exponent laws when possible.

    1. root of k^2/3
    my answer:

    = (k^2/3)^1/2

    = and then?

    2. root of ab^2
    my answer:

    = (a)^1/2 (b^2)^1/2

    = a^1/2 b^1

    3. 4 root of 81 x^8 y^12
    my answer:

    = (81)^1/4 (x^8)^1/4 (y^12)^1/4

    = 81^1/4 x^2 y^3

    4. cube root of x and square root of x
    my answer:

    = (x)^1/3 (x)^1/2

    = x^2/6+3/6

    = x^5/6

    Is that right or not? Explain please. Thanks.
    Why in the world donít you learn basic LaTeX?
    1) [TEX]\sqrt[3]{k^2} [/TEX] gives  \sqrt[3]{k^2}

    2) [TEX]\sqrt{ab^2} [/TEX] gives  \sqrt{ab^2}

    3) [TEX]\sqrt[4]{81x^8y^{12}} [/TEX] gives  \sqrt[4]{81x^8y^{12}}

    4) [TEX]\sqrt[3]{x\sqrt{x}} [/TEX] gives  \sqrt[3]{x\sqrt{x}}
    Last edited by Plato; September 5th 2012 at 04:49 PM.
    Thanks from ford2008
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  3. #3
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    Re: Express radicals in exponential form.

    Hey Plato,

    I will learn basic LaTeX. Had no time yet to start.
    Your No. 1 should be just a square root of k^2/3 not a cube root.

    So could you tell me if my answers are right or whats wrong?
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  4. #4
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    Re: Express radicals in exponential form.

    Quote Originally Posted by ford2008 View Post
    Your No. 1 should be just a square root of k^2/3 not a cube root.
    So could you tell me if my answers are right or whats wrong?
    That may be your whole problem! You do not understand the notation.

    k^{\frac{2}{3}}=\sqrt[3]{k^2}. Thus it is a cube root.

    For any fractional exponent k^{\frac{M}{N}}=\sqrt[N]{k^M}.
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  5. #5
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    Re: Express radicals in exponential form.

    Thank you. I think I got it now.
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