# Rules for dividing exponents

I know that x^3/x^2=x but what would x^2/x^3 equal?  Would it be x^-1 or just x?

Do you just take the difference between the two exponents or do you subtract them left to right?
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Commented:

Subtract left to right (in your notation).
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Commented:
>> what would x^2/x^3 equal?  Would it be x^-1
x^2/x^3 = (x*x) / (x*x*x) = 1/x = x^(-1)

Most exponent rules are easy to verify with a simple expansion as above.
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Commented:
If you ever get stuck on a similar problem, try plugging in numbers and see what makes sense.

Let's plug 10 in for x in your original question and see what happens:
I know that 10^3/10^2=10 but what would 10^2/10^3 equal?  Would it be 10^-1 or just 10?

or

I know that 1000/100=10 but what would 100/1000 equal?  Would it be 1/10 or just 10?

Now you have both the answer and the reason behind the answer.
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