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This follows directly from the law for multiplication. For instance (using the symbol "^" for power):

10^3 x 10^2 = 10^5

Here, the exponents are added. Rearranging the multiplication, you get a division:

10^5 / 10^3 = 10^2

(Just like 6 / 2 = 3 follows from the fact that 2 x 3 = 6, for example.)

As you can see, it is obvious that the exponents must be subtracted in this case. If you want the more general case, take any multiplication with exponents (using the same base):

x^a times x^b = x^(a+b)

Rearranging to form a division:

x^(a+b) / x^a = x^b

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When dividing two terms with the same base you what the exponents.?

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