M098 Carson Elementary and Intermediate Algebra 3e Section 10.2
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1 M09 Crso Eleetry d Iteredite Alger e Sectio 0. Ojectives. Evlute rtiol epoets.. Write rdicls s epressios rised to rtiol epoets.. Siplify epressios with rtiol uer epoets usig the rules of epoets.. Use rtiol epoets to siplify rdicl epressios. Voculry Rtiol Epoet A epoet tht is frctio. Prior Kowledge Epoet Rules: 0 =, where is ideterite Frctio Opertios: Add, sutrct, ultiply New Cocepts. Evlute rtiol epoets. Up to this poit we hve used our rules for epoets with iteger epoets. Now we eted the to rtiol (frctio) epoets s well. Wht would rtiol epoet e? Let s look t couple of eples: (6) / = ( ) / = / = = Wht other opertio o 6 will give for result? () / = ( ) / = / = = Wht other opertio o will give for result? These re the se results we would get if we were to tke the squre root of the uer. () / = ( ) / = / = = This result is the se s tkig the cue root (third root) of. (6) / = ( ) / = / = = This result is the se s tkig the fourth root of 6. The deoitor of the frctiol epoet is the se s the ide of the rdicl. This is siply ew ottio for filir cocept. V. Zrocki 0 pge
2 M09 Crso Eleetry d Iteredite Alger e Sectio 0. Eple : Rewrite i rdicl ottio d evlute if possile. / / / / c. d. 9 9 / e. f. / g. / w So fr ll the rtiol epoets hve hd oe i the uertor. Wht would frctio e tht hs uer other th? Agi, let s look t soe eples, reeerig tht the rules we lredy kow ust e cosistet. / = ( / ) = = The uertor is the power to which we rise the root. Notice it does ot tter if we do the power or the root first. / = ( ) / = 6 / = Geerlly it is etter to do the root first ecuse the uers re sller. I geerl, for /y, (the uertor) represets the power d y (the deoitor) represets the root. Just keep reidig yourself: power over root. (The root of tree grows o the otto.) Eple : Rewrite i rdicl ottio d evlute if possile. / w / / c. Not rel uer / d. Either swer is correct ut the lst oe is etter for. e. / f. / 6 / / / 7 g. h. r r / 7. Write rdicl epressios i epoetil for. If the epressio is give i rdicl for, it c e rewritte i epoetil for y reversig the process. Eple : Rewrite i epoetil for.. /. 7 / 7 r r V. Zrocki 0 pge
3 M09 Crso Eleetry d Iteredite Alger e Sectio 0. c. / 7 7 / 7 / d.. Use rules of epoets to siplify epressios with rtiol epoets. Mth is cosistet so ll of the epoet rules tht we lredy kow ust still pply to rtiol epoets. We coie our frctio rithetic skills d epoet skills to siplify these proles. Eple : / / 6 6 To ultiply powers, use the product rule: Keep the se d dd the epoets. To dd frctios, fid coo deoitor. / 6 Eple : c / c / c c 0 0 Multiply the coefficiets d use the product rule: Keep the se d dd the epoets. To dd frctios, fid coo deoitor. / 0 c Eple 6: / / To divide powers, use the quotiet rule: Keep the se d sutrct the epoets. To sutrct frctios, fid coo deoitor. / / Eple 7: / To rise power to power, use the power rule: Keep the se d ultiply the epoets. / To ultiply frctios, reduce coo fctors d ultiply the uertors together d the deoitors together. V. Zrocki 0 pge
4 M09 Crso Eleetry d Iteredite Alger e Sectio 0. / Eple : / To rise power to power, use the power rule: Keep the se d ultiply the epoets. Reeer to rise the coefficiet to the power lso. 6 To ultiply frctios, reduce coo fctors d ultiply the uertors together d the deoitors together.. Use rtiol epoets to siplify rdicl epressios. Rtiol epoets llow us to siplify soe rdicl epressios d ultiply d divide rdicls tht hve differet idees. Eple 9: 6 / 6 Rewrite i epoetil for. / 6 Rewrite the se s power. 6 Use the power rule: Keep the se d ultiply the epoets. / 6 Reduce coo fctors d ultiply. Eple 0: Rewrite i rdicl for. / 6 7 Rewrite i epoetil for. / 6 Rewrite the se s power. / Use the power rule: Keep the se d ultiply the epoets. Rewrite i rdicl for. Eple : 0 / 0 Rewrite i epoetil for. / 0 / 0 Use the power rule: Keep the se d ultiply the epoets. / / Reduce the frctios. / Use the power rule i reverse. Rewrite i rdicl for. V. Zrocki 0 pge
5 M09 Crso Eleetry d Iteredite Alger e Sectio 0. Eple : / / Rewrite i epoetil for. / 0 / Chge the frctios to coo deoitor. / Use the product rule. Rewrite i rdicl for. Eple : 6 / 6 / / 6 / 6 Rewrite i epoetil for. Chge the frctios to coo deoitor. / 6 Use the quotiet rule. 6 Rewrite i rdicl for. Eple : / / / Rewrite the outside rdicl i epoetil for. Rewrite the other rdicl i epoetil for. / 0 Use the power rule. 0 Rewrite i rdicl for. V. Zrocki 0 pge
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CHAPTER Sectio.6: Rtiol Epoets Sectio.6: Rtiol Epoets Objectives: Covert betwee rdicl ottio d epoetil ottio. Siplif epressios with rtiol epoets usig the properties of epoets. Multipl d divide rdicl epressios
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