Question Number 43702 by rajesh123456 last updated on 14/Sep/18
![simplify [((12^(1/5) )/(27^(1/5) ))]^(5/2)](Q43702.png)
$${simplify}\:\:\:\left[\frac{\mathrm{12}^{\mathrm{1}/\mathrm{5}} }{\mathrm{27}^{\mathrm{1}/\mathrm{5}} }\right]^{\mathrm{5}/\mathrm{2}} \\ $$
Answered by Joel578 last updated on 14/Sep/18
$$\left(\frac{\mathrm{12}^{\mathrm{1}/\mathrm{5}} }{\mathrm{27}^{\mathrm{1}/\mathrm{5}} }\right)^{\mathrm{5}/\mathrm{2}} \:=\:\frac{\sqrt{\mathrm{12}}}{\sqrt{\mathrm{27}}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$