A drop of liquid of radius $\mathrm{R}={10}^{-2}\mathrm{m}$ having surface tension  $S=\frac{0.1}{4\pi }$ N/m divides itself into K identical drops. In this process the total change in surface energy $\Delta U={10}^{-3}J$  . If K= ${10}^{\alpha }$ . then the value of  $\alpha$ is nearly = _____