EXPONENTIAL RULES - Problem 2

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

Problem 2: Simplify tex2html_wrap_inline115 .

Answer: tex2html_wrap_inline117

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:

displaymath119

Hard Way: Write tex2html_wrap_inline121 as

displaymath123

which in turn can be written

displaymath125

Now write tex2html_wrap_inline127 as tex2html_wrap_inline129
The problem tex2html_wrap_inline115 can now be written

displaymath133


You can check the answer with your calculator. Find the value of tex2html_wrap_inline115 by first finding the value of tex2html_wrap_inline137 and tex2html_wrap_inline139 . The problem tex2html_wrap_inline115 is now simplified to tex2html_wrap_inline143 . Now find the value of tex2html_wrap_inline145 and tex2html_wrap_inline147 . Substitute these values in the expression tex2html_wrap_inline143 to form the expression tex2html_wrap_inline151 which can be simplified to

displaymath153


Now find the value of the answer tex2html_wrap_inline155 . Since the two answers are the same, you have worked the problem correctly.

If you have forgotten what tex2html_wrap_inline157 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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Author: Nancy Marcus

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