Question Number 171739 by Mikenice last updated on 20/Jun/22
$${the}\:{result}\:{of}\:{dividing}\:\left(\frac{{x}^{{a}} }{{x}^{{b}} }\right)^{{a}+{b}} {by}\:\left(\frac{{x}^{{a}+{b}} }{{x}^{{a}−{b}} }\right)^{\frac{{a}^{\mathrm{2}} }{{b}\:}} {is} \\ $$
Commented by kaivan.ahmadi last updated on 20/Jun/22
$$\left({x}^{{a}−{b}} \right)^{{a}+{b}} \:\boldsymbol{\div}\left({x}^{\mathrm{2}{b}} \right)^{\frac{{a}^{\mathrm{2}} }{{b}}} = \\ $$$${x}^{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} } \boldsymbol{\div}{x}^{\mathrm{2}{a}^{\mathrm{2}} } ={x}^{−{a}^{\mathrm{2}} −{b}^{\mathrm{2}} } =\frac{\mathrm{1}}{{x}^{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } } \\ $$
Commented by Mikenice last updated on 20/Jun/22
$${thanks}\:{sir} \\ $$$$ \\ $$