# What is the difference between exponentials and powers?

I am a java programmer. But I have a doubt regarding a mathematics. There was a method called Math.exp(double a) description:Returns Euler's number e raised to the power of a double value. and another method Math.pow(double a, double b) description:Returns the value of the first argument raised to the power of the second argument.. But I am confused what is the difference between the two. I am 15 years and we were told in school that both are the same. But here it seems to be different. Can anyone clear my doubt?

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Euler's number, $e \approx 2.71828$, is very important in many fields of mathematics. An important function that uses this constant is $\exp x = e^x$.

However, $\operatorname{pow}(a, b) = a^b$, a more general case.

You will notice that, if $a=e$,

Math.pow(Math.E, x)


is the same as

Math.exp(x)


Once you are familiar with more properties of $e^x$, you will also note that

Math.exp(b * Math.log (a))


is the same as

Math.pow(a, b)

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thanks for solving by doubt .... I am having my exam today! –  Pranit Bauva Dec 3 '12 at 3:44
The first one computes $e^a$ while the second computes $a^b$. The first is a special case of the second where $a = e$.
In other words, the exponential function $e^a$ has one argument, where the power function $a^b$ allows for two arguments. The exponential function can be viewed as a special case of the second one, and mathematically the exponential function has a nice property for calculus. –  hardmath Dec 2 '12 at 17:00
Analogously $\rm\: double(y) := 2y\:$ is $\rm\:times(x,y) := xy\:$ restricted to $\rm\:x = 2.\ \$ –  Bill Dubuque Dec 2 '12 at 17:49