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1 Lesso -A The Root of the Prole H ow would epoets work if the were fractios? To fid out, we we will use the iteret cocept, where the ase uer represets what the aout of iforatio gets ultiplied ever ear. Sice the epoet represets tie, we will e lookig at situatios where less tha a full ear has passed, so the epoet is a fractio.. Suppose the aout of iforatio availale o the we is ultiplied ever ear. How uch iforatio will e availale ear fro ow?. after two half-ears have passed? = ( = + c. Fid the issig value. d. Therefore,. Suppose the aout of iforatio availale o the we is ultiplied 9 ever ear. How uch iforatio will e availale ear fro ow?. after two half-ears have passed? = 9 c. Fid the issig value. 9 d. Therefore, 9. Supppose the aout of iforatio availale o the we is ultiplied ever ear. How uch iforatio will e availale ear fro ow?. after three / ears have passed? = c. Fid the issig value. d. Therefore,. Supppose the aout of iforatio availale o the we is ultiplied ever ear. How uch iforatio will e availale ear fro ow?. after four / ears have passed? = c. Fid the issig value. d. Therefore, Master Algera OBJ: Itroduce siplifig epressios with epoets -.A
2 . Use the sae kid of reasoig to estiate each of the followig: =. 9 = c. e. = d. 8 = 8 = f. = g. = h. 8 =. The aswers i questio # should see rather failiar! Thik aout these: ecause =. 9 ecause = c. ecause = d. 8 ecause = e. 8 ecause = f. ecause = g. ecause = h. 8 = ecause = Now ou ca see that there is a ver strog coectio etwee fractioal epoets ad roots! Fractioal Epoets Rule # The deoiator of a fractio epoet idicates a root:,, ad i geeral,. Use this epoet rule to evaluate each of the followig: = =. 00 = = c. 00 = = d. = = e. = = f. 8 = = g. = = h. = = 8. Use this rule i reverse to fill i the lak for each prole: 8 =. = c. = d. 0 = e. = f. = g. = h. = Master Algera OBJ: Itroduce siplifig epressios with epoets -.B
3 Lesso -A The Root of the Prole Master Algera OBJ: Itroduce siplifig epressios with epoets -.A
4 Lesso -, cot d The Root of the Power I this activit, we will cotiue to eplore fractios as epoets. I particular, we wat to lear to fid the value of epressios like ad 8.. First, let s practice usig soe of the epoet rules we have alread leared. =. = c. = d. = e. = f.. Now let s appl epoet rules to soe siple fractioal epoets. =. = c. = d. = e. = f. =. Suarize i our ow words what the questios aove deostrate aout how epoets work. = For questios -, we will thik aout what epressios like ad 8 ea i the iteret cotet.. I the epressio, the ase uer eas that the aout of iforatio availale o the iteret gets ultiplied ever. What does the epoet ea?. I a fractioal epoet like, the deoiator idicates a, so we eed to fid the root of the ase, or =. This eas that, so we should ultipl for ever of a ear. Sice we wat ears, or ears, let s just ultipl, three ties: =. Therefore, =.. I the epressio 8, eplai the eaig of the ase (8 ad the epoet.. Fid the root idicated the deoiator of the fractio: =. Now ultipl this the uer of ties idicated the uerator ( : =. Therefore, 8 =. Master Algera OBJ: Epad siplifig epressios with epoets -.C
5 8. Let s put all of these ideas to work with proles ivolvig fractioal epoets. =. c. = = d. e. = f. g. = h. = = = = = = = Now we are read to geeralize how to work with fractios as epoets: Fractioal Epoets Rule # Sice or, these ca also e epressed as or 9. Use these priciples to fid the values elow. =. 8 = c. = d. = e. 9 = f. = g. 8 = h. = i. = j. = k. = l. =. =. = o. 8 = Master Algera OBJ: Epad siplifig epressios with epoets -.D
6 Lesso -B You ve Got The Power! T ie to practice what ou ve leared aout epoets! You should e ale to coplete this page without usig a calculator! Siplif Master Algera OBJ: Practice siplifig epressios with epoets -.E
7 Master Algera OBJ: Practice siplifig epressios with epoets -.F Use properties of epoets to write each epressio with ol oe positive epoet. Show all our steps clearl! ( 0. (. (. 8 ( (. 0 ( z z z z. 0 8 w w w w
8 S Five Epoet, Si Epoet, Seve Epoet, Or iplif each epressio. Use ol positive epoets i our aswers.. a a.. t t p q = 8. p q 9. a 0. c Master Algera OBJ: Review siplifig epressios with epoets Skill -.G
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