POWER TO POWERGlencoe Chapter 1 Real Numbers Lesson 4 Powers of Monomials

OBJECTIVE

• Use the Laws of Exponents to find powers of monomials.

• Previously: We used Laws of Exponents to multiply and divide monomials.

• NOW: We will use Laws of Exponents to find power to power.

• Next: We will use Laws of Exponents to evaluate expressions with negative exponents.

MATHEMATICAL BACKGROUND

• Sometimes the rules for the Power of a Power and the Power of a Product are combined into one rule: (ambn)p = ampbnp

• In general, to simplify an expression involving monomials, write an equivalent expression in which

• each base appears exactly once,• there are no powers of powers, and• all fractions are in simplest form.

EXAMPLE #1

22

22

22

Let start with a cube. How do we find the volume of a cube?

V = BhV = (s)(s)(s)V = s3

V = (22) (22) (22)V = (22)3

V = 26

THINK-PAIR-SHARE

• In the expression (84)3 what does the exponent 3 mean?• What expression represents that situation?

• What is 4 + 4 + 4? • What is another way to write 4 + 4 + 4 using

multiplication?• What is (84)3 simplified? • What do you think the rule is? How is it written?

LET’S TRYSOME TOGETHER

EXAMPLE #2

What do you think will happen when we raise 3m2 to the third power?

CHALLENGE

Simplify: [(73)4]5

Simplify:

HOMEWORK

You are going to be using your textbook for your homework tonight. This book is to go back-and-forth from school to home EVERYDAY!!!!Sometimes, you will need to do the work on notebook paper and NOT on the page in the book. So, know where you put your homework each day.

Page 35 #1-12

TICKET OUT

Pass out the 5 multiple choice questions