Download 8-2/3 - Fort Thomas Independent Schools

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
m
n
For all m and n, and nonzero b, b · b
=b
m+n
.
Power of a Power Property
m n
For all m and n, and all nonzero b, (b )
mn
=b
.
Warm-Up
1. Write 2 xas a decimal when x is an integer from
1 to 10.
2. 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?
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 4· k9 · k 3 · w2 · k.
3. Write (3 8) 3 as a single power.
3 9
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
m
For all m and n, and nonzero b, b = bm-n
.
n
b
1. Evaluate the following.
2. In March 1992, there was a total of 283.9 billion
dollars in U.S. currency in circulation. The
U.S. population was 252.7 million. How much
currency per person was in circulation.
3. Simplify.