Laws of Exponent Lesson 1 Rules of 1 Any number raised to 1 is equal to the number itself x? =x Examples: Common Error: 1. ) 4? = 4 1. ) 4? =4 2. ) 5? = 5 2. ) 5? =5 3. ) 146? =146 3. ) 146? =146 Practice Your Skill! 1. ) 391? = 2. ) 45? = 3. ) 678? = 4. ) 99? = 5. ) 34? = Lesson 2 Product Rule
To multiply two powers having the same base, add their exponents. x? * x? = x??? Examples: Common Error: 1. )a? * a? = a? 1. ) a? * a? = 2a? 2. ) 5x? yz? * 4xy? z? = 5*4x??? + y??? + z??? = 20x? y? z? 2. ) 5x? yz? * 4xy? z? = 9x? y? z? Practice Your Skill! Simplify the following expressions: 1. ) 3y? *4y*3y? = 2. ) 78x? y * -9y? = 3. ) 45b? *11b? = Lesson 3 Power Rule To raise a power, multiply the exponents (x? )? =x?? Examples: Common Error: 1. (ab)? = a? b? 1. ) (ab)? = a??? b??? = a? b? 2. ) (3m? n)? = 3? m??? n??? = 9m? n? 2. ) (3m? n)? =3??? m??? n??? = 27m? n? Practice Your Skill! 1. ) (-3pr? )? = 2. ) (2a? b? )? = 3. ) (6z? t? )? = 4. ) (16c? g? )? = Lesson 4 Quotient Rule If x ? 0 ; m and n are positive integers. Case 1: x? x? = x??? where m > n Examples: Common Error: 1. ) a? a? = a??? = a? 1. ) a? a? = a??? = a? 2. ) a? b? a? b? = a??? b??? = a? b? 2. ) a? b? a? b? = a??? b??? = a13b? Case 2: x? x? 1 where m = n Examples: Common Error: 1. ) a? b? a? b? = 1 1. ) a? b? a? b? = ab 2. ) 3a? *2b? 6a? b? = 6a? b? 6a? b? = 1 2. ) 3a? *2b? 6a? b? = ab Case 3: x? x? = 1x??? where m < n Examples: Common Error: 1. ) a? a? = 1a??? = 1a? 1. ) a? a? = a?? 2. ) 8a? b? 2a? b? =4*1a??? b??? = 4ab? . ) 8a? b? 2a? b? = 4a?? b?? Practice Your Skill! Divide the following monomials using the Quotient Rule. 1. ) a6b3ab2= 2. ) 25x3y45x2y= 3. ) 15a4x5y415a4x5y4= 4. ) m6n4p2m9n3p7= 5. ) k? j? c? k?? j? c? = Lesson 5 Power of a Quotient Rule When a quotient is raised to a power, each number is raised to the same power. xy2= x? y? where y ? 0 Examples: Common Error: 1. ) ab 3= a3b3 1. ) ab 3= a3b3=1 2. ) 2x23y42= 2? x??? 3? y??? =4x? 9y? 2. ) 2x23y42= 4x? 9y? Practice Your Skills! 1. ) m2n34= 2. x7y3z5x2yz45= 3. ) s8f2a7s4fa57= Lesson 6 Zero Exponent Rule Any value, except 0 , raised to zero is equal to 1. x? = 1 Examples: 1. ) 10y? = 10 2. ) f? = 1 Practice Your Skills! 1. ) 110? = 2. ) 74h? = 3. ) c? = Lesson 7 Negative Exponent Rule A number raised to a negative exponent is equal to its reciprocal raised to the opposite positive exponent. x-? =1x? if x ? 0 Examples: Common Error: 1. ) x-7= 1x? 1. ) x-7=x? 2. ) y?? = 1y? 2. ) y?? = y? Practice Your Skills! 1. ) x??? = 2. ) r??? = 3. ) dt?? =
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