Setup and compute the solution to the following problems using exponents.
Billy and Betty are each flipping one coin. Billy flips his three times and Betty flips hers four times. How many possible outcomes are there for Billy? How many possible outcomes are there for Betty? If we consider this all one experiment in which Billy does his part first and then Betty does her part, how many possible outcomes are there altogether?
We know that the number of possible outcomes for Billy is 23 = 8 and the number of possible outcomes for Betty is 24 = 16.
The total number of outcomes for both is 27 = 128. Note that 23 × 24 = 8 × 16 = 128 = 27.
Find the volume using scientific notation.
An astronomer studying a region of space needs to determine the volume of a cubic region whose edges measure 3 × 108 miles long. Find the volume of that region of space.
To find the volume of a cube, we need to cube the length of an edge. For this problem, we would have to compute (3 × 108)3. How can we compute this problem by leaving it in scientific notation? We will solve this problem later in the session after we have formed the necessary properties.
The above two problems motivate the need for properties of exponents to aid in computation. We begin to develop some of the basic properties of exponents. Later in the course, we will extend these properties and develop more properties.
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Date last modified: July 22, 2010.
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By Kris Montis and Timothy Peil
