Property of exponential functions

[Tricky557]

Homework Statement

Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not. I've searched around the internet trying to find properties of adding/subtracting exponential functions, but I couldn't find anything.

 

[sandy.bridge]

You can turn the second term into e^{-\pi s}/e^{-2\pi s}
from there multiply both sides by this denominator. This will reduce both the left and right side to one term. Do they equal?

 

[Ivan92]

Homework Statement

I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not.

This statement is not true. This only applies to multiplication of exponents.

a^xa^y=a^x+y

Refer to this for exponential properties: http://www.efunda.com/math/exp_log/exp_relation.cfm

@Sandy: You are wrong as well. Your equation does not equal to the original problem

 

[Mark44]

Homework Statement

Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if:

e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s))

Is a true statement or not. I've searched around the internet trying to find properties of adding/subtracting exponential functions, but I couldn't find anything.

To answer your question, no, the left side is not equal to the right side.

 

[Mentallic]

@Sandy: You are wrong as well. Your equation does not equal to the original problem

He's not wrong, you just missed the part about him saying "the second term". But I find that advice to be quite useless if it still takes knowledge about exponential properties to determine the correct answer.