# Section 11-1: Properties of Exponents Property of Negatives:

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Section 11-1: Properties of Exponents Property of Negatives:
Suppose m and n are positive integers and a and b are real numbers. Then the following are true: Property Definition Example Β Property of 1: Β Property of 0: Β Property of Negatives: Product Property Β Power of a Power Β Power of a Quotient Β Power of a Product Β Quotient Property π π = b 5 1 = 5 π 0 = 1 7 0 = 1 π βπ = 1 π π 4 β2 = = 1 16 π π π π = π π+π = = 3 6 π π π = π ππ 2 π₯ 2 π¦ 3 = 8 π₯ 6 π¦ 3 π π π = π π π π π₯ 3 π¦ = π₯ π¦ 8 ππ π = π π π π 3π₯π¦ = 9 π₯ 2 π¦ 6 π π π π = π πβπ π₯ 5 π₯ 2 = π₯ or π₯ 3 π₯ 9 = 1 π₯ 6

c. a. b. d. 5-4 e. f. Example 1 Evaluate each expression.
4 5 β = = 4 4 = 256 = = 8 7 a b. = = c. = = 3 d e f. = = 3 6 = 729 (3a-2)3β’3a5 = 27 π β6 3 π 5 = 81 π β1 = 81 π

Example 3 Simplify each expression.
π₯ 2 π¦ π¦ 3 5 a b. (s5t2)3 = π  15 π‘ 6 = π₯ 2 π¦ 5 π¦ 15 = π₯ 2 π¦ 10 Example 3 Simplify each expression. = π 2 = π 2 = 2π 2 a b. = π₯ 2 6 = π₯ 1 3 = π₯ 1 3 = 3 4π₯

Example 4 Evaluate each expression.
= = 3 3 = 27 a b. = β 1 3 = = = 3 Example 5 a. Express using rational exponents. b. Express using a radical. = π  π‘ 10 5 = π  5 π‘ 2 = 2π  5 π‘ 2 20 4 π₯ 3 π¦

π 5 π  15 π‘ 4 Example 6 Simplify: = π 2 π  7 π‘ ππ  = π 2 π  7 π‘ 2 ππ  Example Solve: = 343= π₯ 3 2 = π₯ = x 7 2 = x 49 = x