Question Number 1748 by Rasheed Ahmad last updated on 14/Sep/15
$${Why}\:\:\:{a}^{\mathrm{0}} =\mathrm{1}\:{and}\:\:{a}^{−\mathrm{3}} =\frac{\mathrm{1}}{{a}^{\mathrm{3}} } \\ $$
Answered by 123456 last updated on 14/Sep/15
$$\frac{{a}^{{x}} }{{a}^{{y}} }={a}^{{x}−{y}} ,{a}\neq\mathrm{0} \\ $$$$\mathrm{so} \\ $$$${x}={y} \\ $$$${a}^{\mathrm{0}} ={a}^{{x}−{x}} =\frac{{a}^{{x}} }{{a}^{{x}} }=\mathrm{1} \\ $$$${a}^{−{x}} ={a}^{\mathrm{0}−{x}} =\frac{{a}^{\mathrm{0}} }{{a}^{{x}} }=\frac{\mathrm{1}}{{a}^{{x}} } \\ $$