Rule 2: To divide identical bases, subtract the exponents.
Example 7: Simplify .
Solution: You may combine the base x's, and you many combine the base y's. You may not combine the x, the y, the 3, and the 2 into one entity.
can be written
which in turn can be written .
You can check your answer with a calculator by letting x and y take on any value in the initial problem and in the answer. For example, suppose you let x = 3 and y = 4. The problem can then be written
Now let's substitute 3 for x and 4 for y in the final expression . We have
You have just shown that your answer is correct.
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Author: Nancy Marcus