# Exponents and Monomials Exponents and Monomials Lesson What day is it? Objectives I can use the rules of exponents to simplify moniamials. Monomial is an expression that is a number, a variable, or a product of a number and variables. Constant is a monomial containing no variables. Coefficient is a numerical factor of a monomial.

Degree is the sum of the exponents of a monomials variables. Power is the expression of the form xn. Laws of Exponents Negative Exponents: a n 1 a m n 1 n

a a n n Multiplying Powers: a a a m n Laws of Exponents m Dividing Powers: Power of a Power: Power of a Product: a n

a a a m n m n a ab m mn m m

a b Laws of Exponents n n a a Power of a Quotient: n b b n n a b

bn a 0 Power of Zero: a 1 Examples using the laws of exponents: 1. 2ab 2 5 4 3a b c 6a b 2 3 2. 6x y

12 4 2 3 4 xyz 6x y z x 8 3. 4 x x c 2 4

10x y 2x 4. 4 5xy 5. x 4 2 x 3 6. 2a b 8

4 2 16a 12 8 b 3 n 2 3x y 7. 5 3n 2 x y z 2 3

9 2 2n 2 4 4n 4 x y z x y z 3 3 3 4 n n 8. n 4 64 3 3b

2b 3 3x y x 9. b 3 2 6x y 2y 2 3 2y 8y 2b 6b x x 6