Math- Lesson:- Properties of Eponents
Properties of Eponents What is a power? Power: An epression formed b repeated multiplication of the same factor. Coefficient Base Eponent The eponent applies to the number or variable immediatel to its left, not to the coefficient!!!
Eponents? There s no wa to simplif this anmore. (? ( ( 9 (? In PEMDAS, eponents occur before multiplication. (9 6
Eponents?? Remember how to multipl fractions? 7 8
Your Turn:. ( 6?.? 6. (?.? 8 0
Product of Powers ( ( ( ( ( * ( * * This is used as a factor how man times? ( ( used as a factor five times When ou multipl powers having the same base, ou add the eponents.
Power of a Product ( ( ( * * * * * * m ( m 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!! ( ( (
Product of Powers ( **( ( You can re-arrange the order of multiplication. Coefficients of the powers are handled separatel from the base and the eponent.
Your Turn:. ( (? 0 6. (?
Power of a Power ( ( ( * ( * ( * 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 Power ( ( 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
What is the difference between? ( and ( and ( and ( and ( (
Your Turn: 7. (? 0 8. (? 7 9. (? 8
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 0. ( 6 7. ( w w. ( 6
Your Turn: simplif. ( z 6 8 z. ( m 0 w. ( 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?
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! *
Negative Eponent Propert Possible errors * What is the eponent of the number? Which of these is correct? When ou Grab and drag an term across the boundar line between numerator and denominator, ou just change the sign of the eponent.
Eamples: ( 6 6
Your Turn: ( w z 6. 7. 8. 9. 0 w 6 9 6 9 z
Quotient of Powers * * * * * This is reall a sill propert. We don t even need to memorize this as a separate propert. It s just the negative eponent propert. n m n m * *
Eample: 6 6 * * 6* * 9 Can combine adjacent like based powers using product of powers propert!!!!!! Power of a power propert to remove parentheses.
Eamples: 0 ** *
Eamples: ( 8 CAREFUL!! The base for eponent is just the numerator! ( 8 (power of a power propert * 8 * * 6 0 8** 7 8 8*
Eamples: 0 7 Grab and drag 7 8 0 7 0 7 Product of powers: add the eponents of same based powers
Your Turn: 0.. 9(.. ( ( 7 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!!!!
Power of a Quotient Propert General form of Power of a quotient: m m m This is another sill propert. Isn t it just repeated multiplication of the same factor?
Power of a Quotient Propert 6 General form of Power of a quotient: m n m n m n n * * * * This is another sill propert. Isn t it just the power of a power propert?
Your turn:. Eplain, in our own words, what the negative eponent propert allows ou to do with powers. Include in our answer the words: base, eponent numerator and denominator.
Your Turn:. 6. z 7. 8. 6 z z z z Remember: if ou don t see an eponent, what is the eponent? (
Zero Eponent Propert An base raised to the zero power simplifies to one. 0 000 0 00 0 0 0 ( 0 0 0 0 *
6 0 Eamples: 0 0 0 9 * * * *
Your Turn: 9. 0. 0 z. 8 6 z z