# EXPONENTIAL RULES - Problem 2

Rule 3: When there are two or more exponents to the same base, multiply them.

Problem 2: Simplify .

Solution. You can solve this problem the hard way by using Rule 1 or you can solve it the easy way by using Rule 3.

Easy Way:

Hard Way: Write as

which in turn can be written

Now write as
The problem can now be written

You can check the answer with your calculator. Find the value of by first finding the value of and . The problem is now simplified to . Now find the value of and . Substitute these values in the expression to form the expression which can be simplified to

Now find the value of the answer . Since the two answers are the same, you have worked the problem correctly.

If you have forgotten what means, it means that the actual decimal point is located 39 units to the right of the decimal point in 5.44518. If the exponent of the 10 had been negative, it would have meant that the actual decimal point is located to the left of the decimal point in 5.44518.

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