Question

star A is 4 magnitudes brighter than star B .how does the apparent brightness of star A compare with that of star B?

Answer 1

According to the Pogson's ratio (see https://en.wikipedia.org/wiki/Apparent_magnitude#Calculations) the ratio of the apparent brightness of the stars is equal to:

$$\dfrac{F_A}{F_B} \approx 2.512^{m_A-m_B}$$

where $F_A$, and $F_B$ are apparent brightnesses of the stars A and B respectively, $m_A, m_B$ are magnitudes of these stars. According to the problem statement $m_A-m_B = 4$. Thus:

$$\dfrac{F_A}{F_B} \approx 2.512^4\approx 39.8$$

Answer. Star A is 39.8 times brighter than star B.