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Unit 2 – Exponents & Polynomials Algebra 2A Unit 2 Day A ~ Rules of Exponents WHRHS 2011-2012 Rules & Definitions of Exponents: A. Multiplication - x m x n x m n xm B. Division - n x m n x C. Exponents Raised to Exponents - x m n x m n D. Exponential Expressions Raised to Exponents - x m y n E. 0 as an Exponent - p x m p y n p x0 1 00 undefined 1 xm m x F. Negative Exponents 1 xm m x *Remember negative exponents DO NOT mean negative numbers. *Watch where the parentheses are when you are working with exponents. Everything inside the parentheses is raised to the exponent. Monomial - a Number, a Variable or a PRODUCT of a number and a variable. *monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree of a monomial - is the SUM of the exponents of the variable(s) in the monomial. The degree of a constant term is 0. RULE 1: Multiplying Exponential Expressions: PRODUCT OF POWERS RULE If m and n are positive integers, x m x n x m n Example: Simplify (5a 2b4 )(2ab5 ) Example: Simplify (7 xy3 )(5x2 y 2 )( xy 2 ) WHRHS Unit 2 – Exponents & Polynomials 2011-2012 Algebra 2A RULE 2: Simplifying a Power of an Exponential Expression: POWER OF A POWER RULE If m and n are positive integers, ( x m )n x mn RULE 3: Simplifying Powers of Products: POWER OF A POWER RULE If m,n, and p are positive integers, ( x m y n ) p xmp y np Examples: Simplify the following A) ( x 4 )5 B) ( x 2 ) n C) (2a3b4 )3 D) (2ab)(3a)2 5a(2a 2b) RULE 4: Definition of Zero as an Exponent If x does not equal zero, then x 0 1 . RULE 5: Definition of a Negative Exponent If x does not equal and n is a positive integer, then x n 1 xn RULE 6: Dividing Exponential Expressions: QUOTIENT OF POWER RULE xm If m and n are positive integers, n x m n x 7 x Example: Simplify 3 x RULE 7: Simplifying Powers of Quotients: QUOTIENT OF POWER RULE p xm xm p If m,n, and p are integers and y does not equal zero, then n n p y y a2 Example: Simplify 3 b 2 EXAMPLES: Simplify: 2 3 4 5 A) (3x y )(6 x y ) C) x 2 y 4 x 5 y 2 3a 2b 2 c 1 B) 1 2 4 27a b c 2 Unit 2 – Exponents & Polynomials Algebra 2A WHRHS 2011-2012 Unit 2 Day A Worksheet: 1. (3) 2 2. 5 3 3 3. 7 2 3 5. m 7. x3 2 13. 6. a b c 3 5 2 4 11a 5 10. 3 6c r 3 p rp r p 2 b 15. 2a 3 8. p3 c 6 p5 w pw2 p 3 w3 4 4. 6 w2 x 4 9. w2 x 5 11. 3 2 a b a b 2 5 12. 2 5 5 2 2 5 14. 5 5 x c 16. m m 2 k 1 2 k 2 3 Unit 2 – Exponents & Polynomials Algebra 2A WHRHS 2011-2012 18. y 2n 19. n 2 y 21. 3 x y k x2 17. 2 x k 3 22. 24. a 2 3u 27. 20kn 4k 29. 3a b c 6 a b 3 3 3 1 5 1 10 2 25. 3 32 x y 20. 12 43 2 2 8 3 3 23. 2 3 2 26. 1 2 1 2 n 2 4 2 3 2 c 6 2 3r r 2 2 n 3 28. 2 3 2 4 n 5 22 r 2 s 1 30. 3 2rs 2