Math-00 Lesson - Properties of Eponents
Properties of Eponents What is a power? Power: An epression formed b repeated multiplication of the base. Coefficient Base Eponent The eponent applies to the number or variable immediatel to its left, not to the coefficient!!!
No Eponent? Usuall, we don t write the eponent (saves ink. No Coefficient? * * Usuall, we don t write the coefficient (saves ink. Negative? ( * ( * Usuall, we don t write the coefficient -, we just put the negative smbol (saves ink.
Factor: a number that is being multiplied. means base used as a factor times Base Eponent * * * Product: the result ( answer when multipling.
Power: is repeated multiplication * * * multiplication: is repeated addition
How can ou tell which definition to use? Use the contet of the problem (adding two terms ( ( 7
How can ou tell which definition to use? Use the contet of the problem (adding two terms ( ( 5
How can ou tell which definition to use? Use the contet of the problem * (multipling two terms ( * ( * * * 5
Simplif ( 6 6 (5 50 8
Product of Powers Propert ( ( ( * ( * * This is used as a factor how man times? ( ( used as a factor five times 5 When ou multipl powers having the same base, ou add the eponents.
Power of a Power Propert ( ( ( * ( * ( * This is used as a factor how man times? ( used as a factor si times * ( 6 6 When ou raise a power to another power ( power of a power ou multipl the eponents.
Power of a Product Propert ( ( ( * * * m ( * * * This makes it seem like ou can distribute in the eponent. This onl works with the power of a product! ( You must FOIL the power of a suml!! ( ( m m (
( ( Constants (integer, etc. usuall have an eponent of. 6 8 is a number, we just don t know what it is. You treat all numbers the same (whether the are variables or constants. a b c m ( am bm cm
(? **( ( You can re-arrange the order of multiplication. 5 Coefficients of the powers are handled separatel from the base and the eponent.
(5 ( 5 0 Simplif: ( 5( * 7 0 ( 5 0 ( 5 5 8
What is the difference between? ( and ( and ( and ( and ( (
Watch the negatives! (( 6 8 ( 6 8 6 ( 6 ( 6 8 6 8 8 ( Turn negative signs into multiplication b -. This wa ou will be able to tell if the simplified version is positive or negative. Negative coefficients have an eponent of. A negative number raised to an odd eponent remains negative.
Your Turn: simplif 6 ( z 8 z ( m 5 0 w 5 ( z 8
Negative Eponent Propert Grab and drag * When ou Grab and drag the base and its eponent across the boundar line between numerator and denominator, ou just change the sign of the eponent. Wh do we call this the negative eponent propert?
Eamples: 6 6 6
Negative Eponent Propert Possible errors * When ou Grab and drag the base and its eponent across the boundar line between numerator and denominator, ou just change the sign of the eponent. DO NOT GRAB the coefficient! *
Zero Eponent Propert An base raised to the zero power simplifies to one. 0 000 0 00 0 ( 0 0 0 0 0 0 *
Combination: ( Negative Eponent, ( Product of Powers, ( Power of a Power, ( Power of a Quotient 6 6 * * 6* * 9
Your Turn: 5 ( w z 5 0 w 6 9 6 9 z 5
Eamples: 0 7 0 7 0 7 Grab and drag Product of powers: add the eponents of same based powers 7 8
Your Turn: 5 9( ( ( 7 5 9 7 8
Do ou grab and drag (up or down?? Product of powers propert: add the eponents of like-based powers 6 Product of powers propert: add the eponents of like-based powers 6 Make sure when ou re all done, there are NO NEGATIVE EXPONENTS remaining. 6 It doesn t matter!!!!