# Thread: Is e^x^2 = (e^x)(e^x) ?

1. ## 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.

2. Originally Posted by datanewb
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,

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

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

3. Thank you. I see I was way off!

4. Sometimes you add the indices, sometimes multiply.
There is a clear distinction.
The following is a guide....

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

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