Power Relation in DSB-FC AM
Consider your carrier signal as $E_c\cos W_{ct}$ and your message signal is $E_m \cos W_{mt}$.

The double side band plus carrier signal is, 

$ E_c\cos(W_{ct})+(E_c\cos(W_{ct})E_m\cos(W_{mt})) $

$ E_c\cos(W_{ct})+\frac{1}{2}(E_cE_m[\cos(W_{ct}+W_{mt})+\cos(W_{ct}-W_{mt})]) $

$ Ec*Cos(W_{ct})+\frac{1}{2}E_cE_m\cos(W_{ct}+W_{mt})+\frac{1}{2}*Ec*Em*Cos(W_{ct}-W_{mt}) $

Carrier being $E_c\cos(W_{ct})$

Upper Side band being $\frac{1}{2}E_cE_m\cos(W_{ct}+W_{mt})$ and

Lower Side band being $\frac{1}{2}E_cE_m\cos(W_{ct}-W_{mt})$.

For a signal $A\cos W_t$, the average power is $(\frac{A^2}{R}T)*(\int^T_0 \cos^2 W_t) = \frac{{A_c}^2}{2R}.$

Hence,

Average Power of Carrier is $\frac{{E_c}^2}{2R}$

Average Power of Upper Side band is $\frac{{E_cE_m}^2}{8R}$

Average Power of Upper Side band is $\frac{{Ec*Em}^2}{8R}$