EXPONENTIAL RULES - Rule 3

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

Example 1: tex2html_wrap_inline128 can be written tex2html_wrap_inline130 . According to Rule 1, we can add the exponents. tex2html_wrap_inline130 can now be written tex2html_wrap_inline134 . According to Rule 3, we could have gone directly to the answer by multiplying the exponents

displaymath136


Example 2: Simplify tex2html_wrap_inline138 . According to Rule 3, the answer is tex2html_wrap_inline140 .

Example 3: Simplify tex2html_wrap_inline142 . The expression can be written

displaymath144

You could go directly to the answer by multiplying all the exponents.

displaymath146


Example 4: Simplify tex2html_wrap_inline148 . The solution is as follows:

displaymath150


If you would like to review another example, click on Example.

Work the following problems. If you want to check the answer and review the solution, click on Answer.

Problem 1: Simplify tex2html_wrap_inline152 .

Answer

Problem 2: Simplify tex2html_wrap_inline154 .

Answer

Problem 3: Simplify tex2html_wrap_inline156 .

Answer

Problem 4: If you invested $5,000 in a bank account that pays 12% interest per year compounded monthly, and you leave the money in the account for five years, how much money will be in your account after five years.

Answer

Problem 5: You have $1,000 in your account and will need $3,000 in ten years. You decide to invest your money in the following manner: You invest the $1,000 for three years at 12% compounded monthly. You then take the proceeds and invest them for one year at 11% compounded weekly. You then take the proceeds and invest them for two years at 10% compounded daily (360 days in a bank year). How much money would you have in the bank after the six years. How much interest will you need to get if you invest the proceeds for the last four years compounded annually?

Answer

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Author: Nancy Marcus

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