5^3 over 5^7 please help, step by step?

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)

step-by-step explanation:

109 is the nearest whole number/final answer! : )