4 minutes Warm-Up Simplify 1) 2) 3) 4)

5.1 Exponents Objectives: To multiply numbers in exponential form To divide numbers in exponential form To simplify expressions with negative exponents

Multiplying Powers with Like Bases For any rational number a, and for all whole numbers m and n,

Example 1 Simplify. Express using exponents. a) b) c) d)

Practice Simplify. Express using exponents. a) b) c) d)

Dividing Powers with Like Bases For any rational number a except 0, and for all whole numbers m and n,

Example 2 Simplify. Express using exponents. a) b) c)

Practice Simplify. Express using exponents. a) b) c)

Negative Exponents For any rational number a except 0, and for all whole numbers m and n,

Example 3 Express using positive exponents. a) b) c) d)

Practice Express using exponents. 1) 2) 3)

The Exponent Zero a0 = 1 for any rational number a except 0.

Example 4 Simplify. a) b) c) d)

Practice Simplify. 1) 2) 3)

Warm-Up 5 minutes Write without exponents. 1) 2) 3) Simplify. Express using exponents. 4) 5)

More with Exponents Objectives: To find a power of a power To find a power of a product or quotient

Raising a Power to a Power For any rational number a, and any whole numbers m and n,

Example 1 Simplify. Express using exponents. (52)3 = 56 (45)6 = 430

Practice Simplify. Express using exponents. 1) (54)3 2) (22)5 3) (a6)3 1) (54)3 2) (22)5 3) (a6)3 4) (n4)4

Example 2 Simplify. (5x)3 = (5x)(5x)(5x) = 125x3 (3z)2 = (3z)(3z) = (2y2)(2y2)(2y2)(2y2) = 16y8

Practice Simplify. 1) (3y)2 2) (6m)4 3) (2a3)3 4) (4x3)2

Example 3 Simplify. (4x5y2)3 = 43x15y6 = 64x15y6 (-2x5y2)7 = -27x35y14 = (2y2)(2y2)(2y2)(2y2) = 16y8

Practice Simplify. 1) (4y3)4 2) (3x4y7z6)5 3) (-7x9y6)2

Example 4 Simplify.

5 minutes Warm-Up Simplify 1) (34)3 2) (6x)3 3) (3x5)4 4) (-3m4n2)2 5)

Multiplying and Dividing Monomials Objectives: To multiply and divide monomials

Example 1 Multiply. (7y)(2y) = (7)(2)(y)(y) = 14y2 (5a3)(3a2) (-3x3)(4xy5) = (-3)(4)(x3)(x)(y5) = -12x4y5

Practice Multiply. 1) (3x)(-5) 2) (-m)(m) 3) (-x)2x3 4) (3p5q2)(4p2q3)

Practice Multiply. 5) (4x5y5)(-2x6y4) 6) (-7y4)(-y)(2y3) 7) (7a5)(3a3)(-a5) 8) (9b2)(2b5)(-3b7)

Example 2 Divide. 3 a 5 = 4 3 b 2 = a 2

Practice Divide. 1) 2) 3) 4)