# Exponents and Monomials

Exponents and Monomials 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

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