Explanation

(d) In a common-emitter configuration, the voltage gain is defined as the ratio of change in the output voltage to the change in the input voltage.
$A_{V} = \beta \times$ resistance gain …(i)
Also, power gain is defined as the ratio of the change in the output power to the change in input power.
$A_{p} = \beta^{2} \times$ resistance gain …(ii)
Dividing Eq. (ii) by Eq. (i), we get
$\frac{A_{p}}{A_{V}} = \ \beta$