Tuesday June 17: Laws of Exponents

Definitions Monomial: a number, variable, or the product of a number and one or more variables Constant: number

32 · 34 = 3 · 3 · 3 · 3 · 3 · 3 = 36

Product of Powers To multiply two powers that have the same base, add the exponents. Example: xa · xb = xa+b

Examples: Example 1: (5x6)(x3) = 5·x·x·x·x·x·x · x·x·x = 5x9 or 5x6+3 = 5x9 Example 2: (4ab3)(-7a2b2) = 4·a·b·b·b · -7·a·a·b·b = 4·-7·a·a·a·b·b·b·b·b = -28a3b5 or -28a1+2b3+2 = -28a3b5

(k2)4 = k2·k2·k2·k2 = k2+2+2+2 = k8

Power of a Power When you have an exponent raised to another exponent, multiply the exponents. Example: (am)n = km·n

(xy)4 = xy·xy·xy·xy = x4y4

Power of a Product When you have an product raised to an exponent, apply the exponent to each factor. Example: (ab)m = ambm

Example: (-2a4b2)3 = (-2)3(a4)3(b2)3 = -8a12b6

Practice

NOTE!!! (-2)3 = -8 (-2)4 = 16 -23 = -8 -24 = -16

Your turn! p.173 #1-37 odd

Laws of Exponents Continued

Example: = =

Quotient of Powers To divide two powers that have the same base, subtract the exponents. Example: = =

Examples: Example 1: Example 2: = = = =

Practice

Your turn! p.213 #1-29 odd

Negative Exponents

51 5 50 1 1 = = 51 5 So any base to the power 0 equals 1. Examples:

a-3 a3 a0 · = = 1 So that must mean… · a3 So a negative exponent means…flip it and change the exponent to positive

Examples = 1 1 = = 21 b3 2b3

Practice Express without any negative exponents.

Your turn! p.218 #1-7 odd, 21-41 odd