Question

Communicate Mathematical Ideas Why do you subtract exponents

when dividing powers with the same base?

Answer 1

We subtract exponents when diving powers with the same base because they eventually get canceled out when written in expanded form.

Explanation:

For example, if we expand the given fractions:

10^3/10^1 = 1000/10 = 100 = 10^2

Now, if we subtract the exponents we get the same result.

10^3-1 = 10^2

So, a^m/a^n = a^m-

n is one of the exponent rules which saves time and makes calculation easier.