ExponentRulesandExamples

ExponentRulesandExamples - = Every factor is raised to...

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Exponent Rules and Examples A Zero Exponent Rule 1 0 = a Examples: 1) 1 12 0 = 2) 1 ) ( 0 = xyz 3) wr wr wrv 4 ) 1 ( 4 4 0 = = 4) 5 4 1 4 6 0 = + = + 5) 6 1 ) 1 ( 6 6 0 0 = = h x B Negative Exponent Rules n n n n n n a b b a a a a a = = = - - - 1 1 Examples: 1) 81 1 ) 3 ( 1 ) 3 ( 4 4 = - = - - 2) c a b c b a 2 3 3 2 2 2 = - - Notice: Only factors with negative exponents were 'moved'. 3) 8 2 2 3 3 3 x x x = = - 4) 3 5 3 2 5 5 3 2 16 4 4 m p n m p n p n m = = - - Caution: 2 4 - is not a negative number. A negative exponent does not necessarily mean the value is negative. Think reciprocal rather than negative. C Product Rule n m n m a a a + = (bases must be the same) Examples: 1) 5 8 5 2 4 4 r r r r = - 2) 2 8 3 2 8 3 2 3 4 5 2 ) )( ( z y x z y x z xy z y x = = - - 3) 11 11 2 11 1 2 10 4 1 2 2 9 1 3 1 3 3 ab ab b a a b a b a = = = - - - - - - -
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D Quotient Rule n m n m a a a - = (bases must be the same) Examples: 1) 64 1 4 1 4 4 4 3 3 8 5 = = = - 2) 2 5 2 5 6 2 4 3 k h k h k h k h = = - - 3) 3 12 3 12 2 8 8 5 4 2 5 6 4 3 3 2 4 1 4 2 2 2 2 y x y x y x y x y x y y x y x = = = - - - - - Notice: Product rule was used across first, then quotient rule. E Power Rules ( ) mn n m a a = Power to a Power: Multiply exponents ( ) n n n b a ab = or n n n b a b a
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Unformatted text preview: = Every factor is raised to exponent outside parentheses. Examples: 1) ( ) 8 6 6 8 2 3 2 4 ) ( s r r s r s = =--2) ( ) 8 4 8 2 6 2 2 10 6 1 2 2 2 5 3 1 b m b m m m b b m m b b m = = = ----When simplifying, product and quotient rules were used. 3) 12 4 2 12 4 2 2 2 6 2 25 5 ) 5 ( c b a c b a c ab = =--4) 3 6 51 3 6 36 15 3 36 6 15 3 1 12 2 5 z y x z y x x z x y x z x y x = = = -----When simplifying, negative exponent and product rules were used. These rules only involve multiplication, division, and powers; not addition or subtraction. n m n m a a a + + n m n m a a a--...
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ExponentRulesandExamples - = Every factor is raised to...

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