**Solution:**

To divide the exponents with the same base, we use the rule for dividing exponents which says: a^{m}/a^{n} = a^{m - n}

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.

Therefore, we subtract exponents when dividing powers with the same base because they are eventually canceled out when written in the expanded form.

## Why do you subtract exponents when dividing powers with the same base?

**Summary:**

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