Big Idea Because of the relationship between repeated multiplication and powers, products & powers of powers can be themselves written as powers. Product of Powers Property For all m and n, and nonzero b, b · b = b. m n m+n Power of a Power Property For all m and n, and all nonzero b, (b ) = b. m mn n

Warm-Up 1. Write 2 as a decimal when x is an integer from 1 to Multiply any two of the first five numbers in your list of answers for Question 1. The product will also be in the list. Why is this? 3. Repeat Questions 1 and 2 with 3x instead of 2x. Does the same pattern hold? x

Additional Examples 1. A collector started with 2 antique pocket watches, and every year his number of pocket watches doubled. Write an expression for the number of pocket watches the collector has after d years, and then after 5 more years. 2. Simplify w · k · k · w · k. 3. Write (3 ) as a single power. 4. Simplify 2g(g )

Big Idea Because of the relationship between multiplication and division, quotients of powers can be themselves written as powers. Quotient of Powers Property For all m and n, and nonzero b, b = b. b m n m-n

1. Evaluate the following. 2. In March 1992, there was a total of billion dollars in U.S. currency in circulation. The U.S. population was million. How much currency per person was in circulation.

3. Simplify.