Answer:
1 / 5^4 (or 1 / 625)
Step-by-step explanation:
The easiest way to understand and solve this is by expanding everything:
5^3 = 5*5*5
5^7 = 5*5*5*5*5*5*5
Now put those over each other like this:
5*5*5
-----------------------
5*5*5*5*5*5*5
Then I essentially draw "1"s or lines over each pair of 5s (from the numerator to the denominator) until all of the 5s on the numerator or denominator are used up.
Note: This is completely legal as you are simply dividing pairs of 5/5 to get many 1s, and if you multiply everything by 1, it will eliminate the 1s.
So once you "cross all of them out" you are left with a 1 at the top and 5*5*5*5 at the bottom.
So you can simplify that down to
1 / 5^4 (or 1 / 625, however it's usually not necessary to calculate larger exponents)
