rule
For all numbers x (not zero) and all integers m and n,
ruledivide
rule2pic

When you divide,
and the bases are the same,
you SUBTRACT the exponents.
(top exponent minus bottom exponent)

When in doubt, expand the terms (as shown at the right) to see what is happening.

ruledivide2

ruleDgreen

xab

Examples:

1.  dm1
The bases are the same (both 2's), so the exponents are subtracted.
2.  6neg
The bases can be negative values. The parentheses tell you that the entire negative value is being raised to the power.

3.  341
The bases are the same fraction 3/4, so the exponents are subtracted.
4. 224 
Sneaky one!!!! The bases were not the same in the original problem, but they can be CHANGED to be the same.
4 can be rewritten as 2 squared
.
2new(Multiplication Rule).

5.  525
As was done in Example 4, the bottom number is changed to be compatible with a base value of 5.
6.  21
If the exponents are expressed as variables, simply apply the rule (subtract the variables) and leave the answer in that form.

7.  dm3
The bases are the same (all x's), so the exponents are subtracted.
The numbers in front of the bases are divided.

8. dm4 
Remember: top exponent minus bottom exponent.
Remember: raising to a 0 power creates a 1.

9.  35
The subtraction is always done "top" minus "bottom" exponents. In this problem we get 3 - 5 = -2. This gives us a negative exponent. Remember, with negative exponents, the answer becomes one over the base with the exponent changed to positive.
10.  xbot
Again, subtraction "top" minus "bottom" exponents. In this problem we get 5 - 9 = -4.
The answer becomes one over the base of x raised to the power of +4.
11.    wow
WOW!! This problem combines a multitude of skills to arrive at the final answer.

 

divider

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