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Math Help - Exponents

  1. #1
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    Exponents

    Ok hopefully last time I will bug you guys about exponents .


    Simplify, leave without radicals and negative exponents.

    (sqrt(m+2))(2+m)^3/2


    and



    (sqrt(e^(2x))


    Any help is much appreciated~
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    Ok hopefully last time I will bug you guys about exponents .


    Simplify, leave without radicals and negative exponents.

    (sqrt(m+2))(2+m)^3/2


    and



    (sqrt(e^(2x))


    Any help is much appreciated~
    Try using these rules:
    \sqrt{x} = x^{1/2}

    and
    a^n \cdot a^m = a^{n + m}

    and
    (a^n)^m = a^{n \cdot m}

    -Dan
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  3. #3
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    Quote Originally Posted by JonathanEyoon View Post

    Simplify, leave without radicals and negative exponents.

    A) (sqrt(m+2))(2+m)^3/2

    and

    B) (sqrt(e^(2x))
    Hello,

    to A):

    \sqrt{m+2} \cdot (2+m)^{\frac32} = (m+2)^{\frac12}\cdot (m+2)^{\frac32} = (m+2)^{\frac12 + \frac32} = (m+2)^2

    to B):
    \sqrt{e^{2x}} = \sqrt{\left(e^x  \right)^2} = e^x
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  4. #4
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    Quote Originally Posted by topsquark View Post
    Try using these rules:
    \sqrt{x} = x^{1/2}

    and
    a^n \cdot a^m = a^{n + m}

    and
    (a^n)^m = a^{n \cdot m}

    -Dan


    Ok using the rules you gave me, I think I figured out the first one

    (sqrt(m+2))(2+m)^3/2

    is the same as

    ((m+2)^(1/2))((m+2)^(3/2)) = (m+2)^2. If this is correct, from here should I foil?


    For the second one...

    Can I have a little help starting off
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  5. #5
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    Quote Originally Posted by earboth View Post
    Hello,

    to A):

    \sqrt{m+2} \cdot (2+m)^{\frac32} = (m+2)^{\frac12}\cdot (m+2)^{\frac32} = (m+2)^{\frac12 + \frac32} = (m+2)^2

    to B):
    \sqrt{e^{2x}} = \sqrt{\left(e^x  \right)^2} = e^x

    Hi thanks for the answer!! But I still don't understand how you got the answer for part B . Could you walk me through it?
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    (sqrt(e^(2x))
    \sqrt{e^{2x}} = \left ( e^{2x} \right ) ^{1/2}

    Does this help?

    -Dan
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    Ok using the rules you gave me, I think I figured out the first one

    (sqrt(m+2))(2+m)^3/2

    is the same as

    ((m+2)^(1/2))((m+2)^(3/2)) = (m+2)^2. If this is correct, from here should I foil?
    Check with your teacher, but this form is probably fine.

    -Dan
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  8. #8
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    Quote Originally Posted by topsquark View Post
    \sqrt{e^{2x}} = \left ( e^{2x} \right ) ^{1/2}

    Does this help?

    -Dan


    Thanks!!! That helped quite a bit!
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  9. #9
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    Hey final one!!.... I think haha


    [35(2b+1)^(3) / 7(2b+1)^(-1)]^2



    I factored out a 7 and did some other stuff leaving


    [5(2b+1)^(4)]^2


    From here I'm stuck
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  10. #10
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    Quote Originally Posted by JonathanEyoon View Post
    [35(2b+1)^(3) / 7(2b+1)^(-1)]^2

    I factored out a 7 and did some other stuff leaving

    [5(2b+1)^(4)]^2


    From here I'm stuck
    Hello,

    your result is correct. Now use :

    (a \cdot b^n)^m = a^m \cdot b^{nm}

    For confirmation only: 25 \cdot (2b+1)^8
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  11. #11
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    Quote Originally Posted by earboth View Post
    Hello,

    your result is correct. Now use :

    (a \cdot b^n)^m = a^m \cdot b^{nm}

    For confirmation only: 25 \cdot (2b+1)^8


    From 25(2b+1)^8

    Is that the simpliest form?
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  12. #12
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    Quote Originally Posted by JonathanEyoon View Post
    From 25(2b+1)^8

    Is that the simpliest form?
    Hello,

    I don't know a way to simplify this term, so this result must be sufficient.

    In short: Yes.
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