# Equivalent Algebraic Expressions.

• November 5th 2013, 12:51 PM
sepoto
Equivalent Algebraic Expressions.
I am trying to see right now how these became equivalent:

$\frac{1}{2}((x-a)^2+y_0^2)^-^1^/^2(2(x-a))=\frac{x-a}{\sqrt(x-a)^2+y_0^2}$

• November 5th 2013, 12:56 PM
SlipEternal
Re: Equivalent Algebraic Expressions.
$x^{-k} = \dfrac{1}{x^k}$ and $x^{1/n} = \sqrt[n]{x}$ (where $k$ is any real number and $n$ is a positive integer). Do you see it now?
• November 5th 2013, 01:06 PM
sepoto
Re: Equivalent Algebraic Expressions.
$\frac{1}{2}*\frac{2(x-a)}{((x-a)^2+y_0^2)^1^/^2}$?

• November 5th 2013, 01:48 PM
HallsofIvy
Re: Equivalent Algebraic Expressions.
Quote:

Originally Posted by sepoto
I am trying to see right now how these became equivalent:

$\frac{1}{2}((x-a)^2+y_0^2)^-^1^/^2(2(x-a))=\frac{x-a}{\sqrt(x-a)^2+y_0^2}$

I presume you know that $\frac{1}{2}(2)= 1$. You should also know that $A^{1/2}= \sqrt{A}$ and $A^{-1/2}= \frac{1}{A^{1/2}}= \frac{1}{\sqrt{A}}$