Title: Lesson 2-8
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 2-9

Example 1 Write Expressions Using Powers
Write 2 ∙ 2 ∙ 2 ∙ 2 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 using exponents.

2 ∙ 2 ∙ 2 ∙ 2 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7
= (2 ∙ 2 ∙ 2 ∙ 2) ∙ (7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7)		Associative Property
= 2^4 ∙ 7^6					Definition of exponents

Example 2 Write Expressions Using Powers
Write x ∙  x ∙  x ∙  y ∙  y ∙  y ∙  x using exponents.

x ∙  x ∙  x ∙  y ∙  y ∙  y ∙  x = x ∙  x ∙  x ∙  x ∙  y ∙  y ∙  y	Commutative Property
			 = (x ∙  x ∙  x ∙  x) ∙ (y ∙  y ∙  y)	Associative Property
			 = x^4 ∙ y^3			Definition of exponents

Example 3 Evaluate Powers
Evaluate 3^5.

3^5 = 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3	Definition of exponents
    = 243		Simplify.

Check using a calculator. 3^5 = 243

Example 4 Evaluate Powers
Evaluate 5^−2.

5^−2 = 		Definition of negative exponents
      = 		Simplify.

Example 5 Evaluate Powers
ALGEBRA  Evaluate x^3 ∙ y^2 if x = 2 and y = 4.

x^3 ∙ y^2 = 2^3 ∙ 4^2			Replace x with 2 and y with 4.
          = (2 ∙ 2 ∙ 2) ∙ (4 ∙ 4)	Write the powers as products.
          = 8 ∙ 16			Simplify.
          = 128			Simplify.