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The reason is because you get the same answer, if you take x^3 divided by x^2 you will get x^1 which is x. An example, allow x to be 2, 2^3=8 2^2=4. 8 divided by 4 is 2, which x is, in the example. If you are looking for a more in depth answer, the reason why it works is because exponents are basically multiplications, as you should know, so 2X2X2 when divided by 2X2 is like taking two 2's out of the equation leaving you with 2 or x, as in the example. Again, 2^3 is basically 2X2X2, so if you are dividing by 2^2, 2X2, cross out the numbers, and you are left with one two, the answer, from the example.

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Q: Why do you subtract when you divide exponents?
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