Power fractions

Problem:



$ \frac{12^9}{12^2} $

Solution:

When you divide, power subtracts, so think of

$ \frac{12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12}{12  \times 12} = 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 = 12^7 $.

Or more succinctly, $ \frac{12^9}{12^2} = 12^{9-2} = 12^7 $.