اگر $\frac{a}{b}=\frac{c}{d}$ باشد، کدام رابطه برقرار است؟ $(m,n\in \mathbb{Z},x,y\in \mathbb{R})$

${{(\frac{ma+nc}{mb+nd})}^{۲}}={{(\frac{ax}{by})}^{۲}}$

${{(\frac{ma+nc}{nb+md})}^{۳}}=\frac{{{(ax)}^{۳}}+{{(cy)}^{۳}}}{{{(bx)}^{۳}}+{{(dy)}^{۳}}}$

 $\frac{{{a}^{۲}}+{{c}^{۲}}}{{{b}^{۳}}+{{d}^{۳}}}={{(\frac{ma+nc}{mb+nd})}^{\frac{۲}{۳}}}$

${{(\frac{ma+nc}{mb+nd})}^{\frac{۳}{۲}}}=\frac{{{(ax)}^{\frac{۳}{۲}}}+{{(cy)}^{\frac{۳}{۲}}}}{{{(bx)}^{\frac{۳}{۲}}}+{{(dy)}^{\frac{۳}{۲}}}}$