1. Section 1.4 Objectives: Use the properties of exponents This section is prepared by M. Zalzali Positive Integer Exponents

2. Repeated Form and Exponent form Exponents are used as a short-hand form for repeated multiplication. Instead of writing We write Repeated Form Exponent Form Note “a” has been repeated 5 times, that’s why we wrote a 5 is read “ a to the fifth power’ a = Base, 5 = Power,

3. Example 1 Fill out the table with the correct answer (3x-1)(3x-1) (2x+9)(2x+9)(2x+9) (2x)(2x)(2x) b6b6 Exponent FormRepeated Form

4. Rules and Properties of Positive Integer Exponents For any real number a and natural numbers m and n.n. Example 1 First property Simplify each expression. ( Write in exponent form )

5. … Simplifying Expressions Note: When we multiply two expressions, we have to take into consideration the associative and commutative properties of multiplication when needed. Example 2 Simplify the product Class Exercise Simplify the product

6. … For any real number a,and natural numbers m and n.n. m > n Second Property Example 3 Simplify the expressions

7. … For any real number a and natural numbers m and n.n. Third Property Example 4 Simplify the expressions

8. … For any real number a and b, Fourth Property Example 5 Simplify the expressions (a) (b) (c) and natural number m

9. … For any real number a and b, and natural number m Fifth Property Example 6 Simplify the expressions (a) (b)

10. … Class Exercise Simplify the expressions

11. … For any real number a Zero Exponent Example 7 Simplify the expressions

12. Home Work Do the selected exercises from the syllabus Section 1.4 The end