Is there a way to simplify a^log n, a = 1 / b

1. Sep 14, 2011

jstep

Is there a way to simplify a^logn, a = 1 / b

I don't know if this is possible, but I thought I would ask for another opinion if i'm overlooking something. Anyway, is there a way to simplify alogbn, a = 1 / b

2. Sep 14, 2011

MisterX

Re: Is there a way to simplify a^logn, a = 1 / b

yes

$\left(b^{-1}\right)^{log_{b} n} = \left(b^{log_{b} n}\right)^{-1} = n^{-1}$

as

$\left(b^{x}\right)^{y} = \left(b^{y}\right)^{x}$

Last edited: Sep 14, 2011
3. Sep 14, 2011

jstep

Re: Is there a way to simplify a^logn, a = 1 / b

aha! thanks!