Priya wears +1.5 D glasses to achieve normal vision from 25 cm...

Let the near point of Priya's eye without glasses be $D'$.

Using the lens formula for her glasses to achieve normal vision from $25 \text{ cm}$ ($u = -0.25 \text{ m}$):

$P = \dfrac{1}{v} - \dfrac{1}{u}$

$1.5 = \dfrac{1}{-D'} - \dfrac{1}{-0.25}$

$1.5 = -\dfrac{1}{D'} + 4$

$\dfrac{1}{D'} = 4 - 1.5 = 2.5 \text{ m}^{-1}$

$D' = \dfrac{1}{2.5} \text{ m} = 0.4 \text{ m} = 40 \text{ cm}$

The focal length of the simple microscope lens is:

$f = \dfrac{1}{P_{m}} = \dfrac{1}{20} \text{ m} = 5 \text{ cm}$

The maximum magnifying power of a simple microscope is obtained when the final image is formed at the near point of the observer. Since Priya uses the microscope without her glasses, her near point is $D' = 40 \text{ cm}$.

The maximum magnifying power $m$ is given by:

$m = 1 + \dfrac{D'}{f}$

$m = 1 + \dfrac{40}{5}$

$m = 1 + 8 = 9$