Lesson 12-6

Example 1 Multiply Powers
Find 33 · 3. Express using exponents.

33 · 3 = 33 · 31	3 = 31	Check  33 · 3 = (3 · 3 · 3) · 3
	= 33 + 1	The common base is 3.	= 3 · 3 · 3 · 3
	= 34	Add the exponents.	= 34  

Example 2 Multiply Monomials
Find –2x3(3x4). Express using exponents.

–2x3(3x4) = (–2 · 3)(x3 · x4)	Commutative and Associative Properties
	= (–6)(x3 + 4)	The common base is x.
	= –6x7	Add the exponents.

Example 3 Divide Powers
Find . Express using exponents.

 = 57 – 3	The common base is 5.
	= 54	Simplify.

Example 4 Divide Powers
Find . Express using exponents.

 = m10 – 2	The common base is m.
	= m8	Simplify.

Example 5 Real-World Example
SCIENCE A petri dish contains 105 bacteria after one hour. After four hours, there are 1010 bacteria in the dish. How many times more bacteria are in the dish at four hours than at one hour?

To find how many times more bacteria, divide 1010 by 105.

 = 1010 – 5	Quotient of Powers
	= 105	Simplify.

The number of bacteria from one hour to four hours is 105 or 100,000 times as much.