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When dividing exponents do you subtract them? Yes
When dividing exponents with like bases you subtract the exponents. 

Also, when you have like bases you divide the coefficients, and subtract the exponents.

Dividing negative exponents

Dividing uses the same rules whether the exponents are positive or negative. If you are multiplying like bases then add the exponents. If you are dividing you subtract the exponents. Use your signed number rules for adding and subtracting, and remember to always write your final answer with positive exponents.  

If you end up with a negative exponent you flip it to the opposite side of the fraction in order to create the reciprocal of the negative exponent. I always teach that if the negative exponent is downstairs you move it upstairs, and if the negative exponent is upstairs you move it downstairs.

                                                    Move the x^3 to the denominator (downstairs)    

                                                        With parenthesis the exponent applies to 
                                                         the coefficient and variable.

In the example above: The x^-3 moves downstairs, and the (2y)^-4 moves upstairs. Remember with parenthesis the exponent applies to the coefficient and variable.

Dividing exponents with different bases
You cannot combine exponents if the bases are different

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Related websites/Dividing Exponents

Dividing Exponents/Rapid tables  Nice basic explanation of dividing exponents with like bases,negative exponents,and exponents with fractions.

Dividing Exponents Game  Cool Math has a game that generates practice problems for the division exponent rule and provides solutions

video tutorial dividing exponents
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exponents 81/3 -85/8

How to divide exponents

If you have like bases, you just subtract the exponents. 

Subtract the exponent in the numerator from the exponent in denominator.

 In the example below you would divide the coefficients, and subtract the exponents.
Because there is not a y in the numerator, the y remains in the denominator.
divide exponents x^8/x^3 = x(8-3) =x^5/ how to divide exponents
dividing exponents 3x^2/y
how do you divide the exponents  15x^3/5xy
Video explains the rules for dividing exponents
Because you have like bases you can             just subtract the exponents. 
You can subtract the exponents even if they are fractions.
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Rules for dividing exponents with like bases.

Applying the Rules for dividing Exponents

What about negative rational exponents?

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In these two examples follow these  rules:

Divide the coefficients, and subtract the exponents.

8x^5/x^4 rules for exponents dividing
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Apply the rules for exponents: Subtract the exponents, and divide the coefficients.
25x^3/5x=5x^2 exponent division
8x^5/2x^2 dividing exponents
Using the rules for exponents you subtract the exponents and divide the coefficients. After subtracting exponents, if you have a negative exponent, flip the exponent in order to create a reciprocal of the negative exponent.
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-6s^2a^5/2s^2a^3 rules for dividing exponents
simplifying negative exponent 1/84/3
Subtract the exponents
dealing with negative exponents 8-4/3
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Watch these two problems, and similar problems in the video here.
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5x^-3/(2y)^-4 =80y^4/x^3 dividing with negative exponents
Create the reciprocal of the negative exponent by flipping the negative exponent to the opposite side of the fraction.
Simplify the fractional exponent. See the video for details on fractional exponents or rules for negative exponents.
Common Core Standard  8.EE.A.1                                                        8th Grade Math
4^5/4^2=4^3 subtract the exponents
Divide the coefficients 12/3=4
Subtract the exponents 8-2=6
Subtract the exponents 3-1=2
5x^-6=5/x^6 your final answer should have positive exponents
2x^-3 = 2/x^3
1/(3x)^-2 = 9x^2 dividing exponents