Is exp(-3ln(x)) equal to x^-3 or -x^3?

[SteveDC]

Homework Statement

Got to part of a problem where I have exp(-3ln(x)) and I am confused as to whether the next step is:

a) exp(ln(x^-3)) = x^-3

or

b) exp(-ln(x^3)) = -x^3


I think the correct step is (a) but not certain, any help would be great :)

 

[SammyS]

Homework Statement

Got to part of a problem where I have exp(-3ln(x)) and I am confused as to whether the next step is:

a) exp(ln(x^-3)) = x^-3

or

b) exp(-ln(x^3)) = -x^3

I think the correct step is (a) but not certain, any help would be great :)

Yes (a) is the correct result.

For (b):

exp(-ln(x^3)) = $\displaystyle \frac{1}{e^{\ln (x^3)}}\$ → $\displaystyle \ \frac{1}{x^3} \ .$

 

[vela]

b) exp(-ln(x^3)) = -x^3

Here it appears you're saying $e^{-a} = -e^a$, that you can simply pull the minus sign out front, which you probably know isn't correct.