EXPONENTIAL RULES - Problem 3

Rule 2: To divide identical bases, subtract the exponents.

Problem 3: Simplify .

Answer: or

Solution: At first glance you might be tempted to say that you can do nothing with the problem because the bases are different. However, you can manipulate the numbers so that you can in fact simplify the above expression.
Recall that 40 can be written as 8 times 5. Rewrite the expression with that substitution. can be written

However the can again be written in a different way. is equivalent to

Is the answer written better than as ? No, just different.

You can check your answer with your calculator.

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