Working with Powers and Exponents

Transcription

1 Working ith Poer nd Eponent Nme: September. 00 Repeted Multipliction Remember multipliction i y to rite repeted ddition. To y +++ e rite. Sometime multipliction i done over nd over nd over. To rite e rite. (red four ured ) men o (red five cubed ) i Prctice: Write the indicted opertion uing eponent. Then perform the opertion. ) b) c) (-.)(-.)(-.) d) e) (-) (-) (-) (-) -(00) (00) (00) (-) (-) (-) (-) (-) f) (ner: ) f f f f Prctice: Perform the indicted opertion. g) h) i) (-) (-0) (-) j) (-) (-) (-) k) (-0) (0.) (0.) Multiplying Remember: ()()() o ( ) nd Eponent Rule ()()()()()() 9 Rule: m n m n + o f f f nd (don t orry ht frctionl eponent men yet.) When multiplying like be, dd the eponent. Prctice: Simplify. ) c c e e yzyz y z yz + + g 9 g b) b b d d f f h h

2 0 c) 0 c c e e g 9 g d) b 00 b 0 d d N N f f h h e) c c e e Ng 9 Ng f) b b d d 9 f (+ ) f h h g) y c c d d g g h) b b d d f f h h i) 9 0 c 0 ( 9 + ) e e c. g. 9. g. j) b b. d d f 9 9 f h 9h Dividing Remember ho to cncel. Mke out of common fctor. r rrrrr rrrrr rr r rrr rrr r h hhh h hhhhhh hhh h ( ) ( ) ( ) ( ) b bb bb // b bbbb bbbb // bb b Rule: m n mn k k k k 0 9 When dividing like be, ubtrct the eponent. Prctice: Simplify. ) b) c) d) e) 0 e e e e t t 0 f f y y r rrrrr rrrrr rr r i the me r rrr rrr r r m m y y 9 k 0k 0 p p b b f f r h h

3 Negtive eponent Notice ht hppen ith the emple Thi led to nother rule. Rule: n nd n n n h hhh h h h hhhhhh hhh h nd d d Prctice: Write ech ner to y, frction ith poitive eponent nd ithout uing frction but uing negtive eponent. f) - or g) z z Dividing Monomil rr 9 rr r r r 9 r r r r h) i) j) k) l) e e 0 0 j 0 j y y t t 0k l k l f f j j 0 mn mn t t k l k l 9 p p t t t t e 9 e m m m y y 9 r r y y 90 t 0 t f e e f 0 Zero Eponent 0 or the poer cncel for n ner of. Rule: 0 Anything to the zero poer i. Prctice: Simplify m) 0 0 (y) 0 (t ) 0 (-+9--) 0 n) 0 e 0 0 (t ) 0 ½ (t ) 0

4 Poer of Poer ( ) uing previou rule. Rule: ( m) n mn An eier y ould be to multiply the nd to get the ne eponent of. Prctice: Simplify. o) ( ) ( ) ( ) ( ) p) ( ) ( ) y ( m ) ( u ) ) ( ) ( ) r ( t ) ( ) r) ( ) bc b c ( def ) ( uvu ) ( ) ) t) y y ( ) ( ) b. ( ) ( 0.. ) y y kl 0k 0 kl k r r b When the rule don t ork Notice: + re not like term nd cnnot be combined. Contrt thi ith. The multipliction cn be done. m + m 9m Don t dd the eponent. m m 0m Do dd the eponent. ) d + d b) e e d d e + e + u + u b u u c) + (-)( ) r +r r (r ) d) (- ) (- )(- ) (- ) (-)(- ) Mied prctice: Simplify e) p p 9 f) g) p p p + ( t ) ( t ) 9 + ( nm ) nm nm y y h) i) + e e + e ( ) ( e )( e )( e) ( ) t t t ( )( )( ) t t t ( ) 9 0

5 Working ith Scientific Nottion Nme: Nov., 00 Scientific nottion i ued to rite very lrge nd very mll number. The ditnce to the un i km or. 0 km. The bcteri Streptococcu pyogene i cm or. 0 - cm long. Lrge Number (poitive poer of 0) Reriting 0, e get Notice: the eponent on the 0 i nd the deciml fter the moved to the right pce moving the deciml right pce.. 0 i cientific nottion nd 0000 i tndrd nottion. Prctice: Write the folloing in tndrd nottion. ) b) c) Rule: 0 m i cientific nottion if < 0 nd m i n integer. ( i beteen nd 0) Note: But only one of thee i in cientific nottion.. i beteen nd 0 o the correct form of the number in cientific nottion i. 0. Although the other number re the me. 0, they re not cientific nottion.. 0 i the cientific form of. To rite in cientific nottion, Move the deciml o only one digit i in front nd drop ending zero... Multiply by ten to the poer tht mtche the number of pce the deciml moved. Prctice: Write the folloing in cientific nottion. d) e) f) Smll Number (negtive poer of 0) Recll: , therefore Dividing by 0000 move the deciml pce to the left. To chnge mll number (negtive poer of ten) in cientific nottion to tndrd nottion, move the deciml to the left the number of pce indicted by the poer of 0. Compre thee: (left) nd. 0 0 (right)

6 Prctice: Write the folloing in tndrd nottion. Wtch the ign. ) b) c) d) To chnge mll tndrd nottion number to cientific nottion, move the deciml fter the firt nonzero digit. Count ho mny pce the deciml moved. Thi i the poer of 0 the number ould be divided by. Mke it negtive eponent. Emple: (((((r. 0 Prctice: Write the folloing in cientific nottion. Wtch the ign. e) f) g) In Rel Life Prctice: Write the miing number. Stndrd Nottion Scientific Nottion ) The popultion of Cnd i. 0. b) The popultion of the orld i bout c) A humn hert i cm in dimeter. d) The dimeter of n rtery i 0.0 cm. e) The moon i. 0 km y. f) The moon m i kg. g) The Erth m i.9 0 kg. h) A hir gro mm per minute. Multipliction nd Scientific Nottion To multiply (. 0 ) (. 0 ), ue the ocitive property (grouping of multipliction doen t mtter) nd the commuttive property (order of multipliction doen t mtter) to get (..) (0 0 ) Emple: ( 0 )(. 0 ). 0 (. 0 ) ( 0 - ). 0 - (. 0 ) (. 0 ). 0 Notice: Wht i rong ith the lt emple? Although the ner i correct, it i not in cientific nottion. To finih the problem, move the deciml one pce left nd incree the eponent by one

7 Look for the pttern! If the deciml move right, the eponent move don If the deciml move left, the eponent move up Prctice: Multiply then rite the folloing in cientific nottion ) ( 0 )(. 0 ) (. 0 )(. 0 )( 0 ) (. 0 )( 0 ) b) (. 0 )(. 0 ) (. 0 )(. 0 9 ) ( 0 )(. 0 ) 9 9 c) ( 0 )( 0 ) Note: The negtive in front of the mke number le thn zero. The negtive in front of the eponent mke mll number. (. 0 )( 0 ) The folloing ill need to hve the deciml moved nd the eponent djuted fter the multipliction. 9 d) (. 0 )(. 0 ) (. 0 )(. 0 ) ( 0 )(. 0 ) 0 e) (. 0 )(. 0 ) (. 0 )(. 0 ) (. 0 )(. 0 ) f) The popultion of the orld i. 0 9 nd the verge peron conume 0 grm of ugr per yer. Ho mny grm of ugr re conumed in the orld per yer? Diviion nd Scientific Nottion. 0. Diviion ork in imilr y ( ) ( ) ( ) Notice the deciml nd eponent Prctice: Divide the folloing then rite the ner in cientific nottion ) b) (. 0 ) (9. 0 ) ( 0 ) ( 0 ) (. 0 ) (. 0 ) c) d).0 0 (. 0 ) ( ) A certin tring of bcteri i. 0 - cm long. There re pproimtely 0 cell in tring Ho ide i ech ingle bcteri? Clcultor nottion Some clcultor ho cientific nottion the me y e hve ritten them here. Some ue EE. They rite. EE to men. 0. Some rite the me thing ith thi in the creen. 0. There re everl y electronic euipment diply cientific nottion. Look in your uer mnul to ee ho it i diplyed on your clcultor.

8 Addition nd Subtrction of Scientific Nottion To combine number through ddition or ubtrction e need to obtin like term, nd ue the ditributive property in revere. To dd (. 0 ) + (. 0 ), e need both poer of 0 to be the me. Chnge one o they both hve the lrger poer of 0 (i.e.. 0 become 0. 0 ). No e hve (0. 0 ) + (. 0 ) The like term re the poer of 0, nd the 0. nd the. re the coefficient. The ditributive property llo u to rerite the ddition : [(0. +.) 0 ]. Giving u the finl ner to be:. 0. Emple:. (. 0 ) + (. 0 ) (. 0 ) + (0. 0 ) (. + 0.) (. 0 - ) + ( 0 - ) ( ) + ( 0 - ) (0. + ) (.0 0 ) (.9 0 ) (.0 0 ) ( ) ( ) Notice: Wht i rong ith the lt emple? Although the ner i correct, it i not in cientific nottion. To finih the problem, move the deciml one pce right nd decree the eponent by one Prctice: Add or ubtrct, then mke ure your ner i in cientific nottion. ) (.9 0 ) + (. 0 ) (. 0 - ) + (. 0 - ) (. 0 9 ) (. 0 9 ) b) ( ) + (. 0 - ) (. 0 ) (.9 0 ) (.9 0 ) (. 0 ) c) (. 0 ) (. 0 ) ( ) ( ) ( ) + (. 0 - ) The folloing ill need to hve the deciml moved before dding or ubtrcting. d) (. 0 ) + (. 0 ) (.09 0 ) + (. 0 ) (. 0 ) (. 0 ) e) (. 0 ) (. 0 ) (. 0 - ) + (. 0 - ) (. 0 ) (9.9 0 ) f) ( ) + ( ) (. 0 0 ) (. 0 ) (. 0 - ) (. 0 - ) g) (. 0 ) (9. 0 ) (. 0 ) + (9.9 0 ) (. 0 ) (.0 0 )

9 Repeted Multipliction ) b) 9 9 c) (-.) -. d) e) (-) -(00) (-) - f) (f) f g) 9 h) i) 00 9 j) - - k) Multiplying ) c 9 e g b) b 9 d f h 0 c) 0 c e 0 g d) b 0 d - f N 9 h e) 0c 9 e N g f) b d f h g) y c 0 d g h) b 9 00d f h i) 9 0 c 0 e.. g j) b. d f h 9 Dividing ) e r y p b) t b c) - m - - f 0 d) f) h) k) e f f e 9 t 0 k e p y t 9h i) 0 l) j l 9k e) g) j k l m) n) 0 t m r y e f j) y 9 n t y z z Poer of Poer o) 0 p) y 00 m u ) r 0 t 0 9 r) b c d 0 e 0 f u v b 0 ) t) y l y k b r When the rule don t ork ) d d 0 + b) e 0 9e u + u u c) r + r 9r d) e) 0 - p 9 p 00t f) - 9n m e e + e 9 p g) y - h) -e - 9 i) t t t

10 Lrge Number ) b) c) d) e) f) Smll Number ) b) c) d) e) f) g) In Rel Life ) b). 0 9 c).9 cm d). 0 - cm e) km f). 0 kg g) kg h) mm/min Multipliction nd Scientific Nottion ) b) c) d) e) f). 0 g Diviion nd Scientific Nottion ) b) c) d). 0 - Addition nd Subtrction of Scientific Nottion ) b) c) d) e) f) g)