Laws of Exponents

Scientific Notation

Powers of Products

Two Motivation Examples:  

Note that the commutative and associative properties were used to rearrange the factors. Further, note that the result has the same exponent on both terms as in the original expression.

Power of a Product. When product of two factors is raised to a power, the result is a product with the two factors each having the same exponent that was the power the expression was raised to.

General Property: (ab)^m = a^mb^m

Examples: (7 · 10)⁹ = 7⁹ · 10⁹

  (3 · 8)⁷ = 3⁷ · 8⁷ 

  (xy)³ = x³y³  

  (ab)⁴ = a⁴b⁴

Examples using more than one law or property of exponents:

Self-Check Problems

Simplify in terms of the exponents

(4 · 10)3	Solution
(3a)4	Solution
(2x2y3)5	Solution

 

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