6.1 Using Properties of Exponents OBJ: To use properties of exponents to evaluate & simplify expressions with powers 6.1 Using Properties of Exponents Do Now: label the parts of this power exponent 3 x x x x = base Rule of Common Bases a b a + b x x x = Like: 3 3 + 2 n n 2 n n 5 = = n n n n n n 5 = Do not copy!

Simplify Ex 1: 1) 4) 2) 5) 3)

( ) ( ) x x n n n (n n n) (n n n) (n n n) n Power to Power Rule = = = ( ) b a ab x x = Like: 2 ( ) 3 3 2 6 n n n = = 2 (n n n) (n n n) (n n n) 6 n Do not copy! = =

Ex 2: Simplify 1) 3) 2) 4)

Zero and Negative Exponents *A negative exponent is an inverse! 1 x -1 = x Ex 3: 1) 2) 3)

Ex 4: 1) 4) 2) 5) 3)

x x x x x x 6.1 continued… Do now: = = or = = OBJ: To use properties of exponents to evaluate & simplify expressions with powers 6.1 continued… Do now: Simplify. x 5 = = x 2 or x 5 = x 2 Quotient of Powers Property x a = x b

Examples: Simplify 1) = = 2) = = = 3) 4)

5) 6)

Power of Quotient Property x a = y a 7) 8)

9)

OBJ: To use exponents and scientific notation to solve real-life problems Scientific Notation - used to write very large or very small numbers expressed in the form... Ex: 3,780,000,000,000 = 12 jumps left 0.00000064 = 7 jumps right