Step 1: Recall magnification principle.
A compound microscope consists of two lenses – the objective lens (magnification $m_1$) and the eyepiece lens (magnification $m_2$).
Step 2: Combine magnifications.
The final magnifying power of the microscope is the product of the magnifications:
\[
M = m_1 \times m_2.
\]
Step 3: Conclusion.
Hence, the magnifying power is $M = m_1 m_2$.