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Math Help - Is e^x^2 = (e^x)(e^x) ?

  1. #1
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    Is e^x^2 = (e^x)(e^x) ?

    Is e^(x^2) = (e^x)(e^x)

    I tried to look up associative properties of exponents, but I'm still unsure about this.

    Thank you.
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  2. #2
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    Quote Originally Posted by datanewb View Post
    Is e^(x^2) = (e^x)(e^x)

    I tried to look up associative properties of exponents, but I'm still unsure about this.

    Thank you.
    No,

    \displaystyle\left(e^x\right)^2=e^x\left(e^x\right  )=e^{x+x}=e^{2x}

    e^{x^2}=e^{x(x)}=\left(e^x\right)^x
    Thanks from datanewb
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  3. #3
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    Thank you. I see I was way off!
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  4. #4
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    Sometimes you add the indices, sometimes multiply.
    There is a clear distinction.
    The following is a guide....

    e^2\left(e^3\right)=[e(e)][e(e)e]=e^5=e^{2+3}

    \left(e^2\right)^3=[e(e)][e(e)][e(e)]=e^6=e^{2(3)}
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