# Simple problem... rearranging fractional exponent expression

• Apr 13th 2010, 02:52 PM
Ares_D1
Simple problem... rearranging fractional exponent expression
This should be simple. Show that

$(\frac{2meE}{h^2})^{1/3}x = (\frac{2m}{h^2 e^2 E^2})^{1/3}eEx$

For some odd reason, I can't seem to get it. Any ideas?
• Apr 13th 2010, 02:58 PM
$(\frac{2meE}{h^2})^{1/3}x = (\frac{2m}{h^2 e^2 E^2})^{1/3}eEx$
$\bigg{(}\frac{2meE}{h^2}\bigg{)}^{1/3}x = \bigg{(}\frac{2meE}{h^2} \cdot \frac{e^2}{e^2} \cdot \frac{E^2}{E^2}\bigg{)}^{1/3}$
$= \bigg{(}\frac{2me^3E^3}{e^2 E^2 h^2}\bigg{)}^{1/3}x = \bigg{(}\frac{2m}{h^2e^2 E^2}\bigg{)}^{1/3}eEx$