To multiply exponential expressions with the same base, keep the base, add the exponents.


 Hortense Flowers
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1 RULES FOR EXPONENTS Epoets re used to write repeted multiplictio of the sme fctor. I the epoetil epressio, the epoet tells us how m times the bse is used s fctor:. Similrl, i the epressio, the epoet tells us there re four fctors of the bse :. Whe ou simplif epoetil epressios, it is importt to uderstd the differece betwee the epressios d (). The lck of pretheses i the epressio mes the epoet ol rises the bse to the d power. So evlutes s ( ). O the other hd, the use of pretheses i the epressio () mes the epoet rises the bse to the d power. So () evlutes s () (). m m +. PRODUCT RULE: To multipl epoetil epressios with the sme bse, keep the bse, dd the epoets. Emples: ) i i We get the sme result whe we dd the powers: + i + + ) pip ip p p Whe epoet is ot writte, the power is. + ( ) ( ) ( ) ( ) ) i A egtive umber rised to eve power is ) () ( ) ( ) ( + + ) Use the ssocitive propert to multipl the coefficiets d dd the vrible powers.. QUOTIENT RULE: m m To divide epoetil epressios with the sme bse, keep the bse, subtrct the epoets. ) Whe the power i the umertor is greter th the power i the deomitor (top hev), the remider goes i the umertor. Emples: i iii ) i Notice, we get the sme result whe we subtrct the power i the deomitor from the power i the umertor: PBCC SLC Lke Worth Mth Lb
2 ( ) ( ) ( ) ( ) ) A egtive umber rised to odd power is egtive. ) ) 9 9 b) Whe the power i the deomitor is greter th the power i the umertor (bottom hev), the remider goes i the deomitor d goes i the umertor whe ecessr. Emples: ) i i i i i i i i We get the sme result whe we subtrct the power i the umertor from the power i the deomitor: ) ) ( ) ( ) ( ) ( ) k k k k ) m m m m ) i The s re bottom hev; the s re top hev. PBCC SLC Lke Worth Mth Lb
3 m. POWER RULE: ( ) m To rise epoetil epressio to power, keep the bse, multipl the epoets. Emples: ) ( ) + + i i We get the sme result whe we multipl the powers: ( ) i i ) ( ) ( ) ( ) ) ( ) i. POWER RULES FOR PRODUCTS AND QUOTIENTS ) Power Rule for Products: (b) b To rise product to power, distribute the power to ech bse d multipl the epoets. Emples: ) ( ) i i i i i i ) ( ) ( ) ( ) p qr p q r p q r p q r Thik: egtive rised to eve power is lws b) Power Rule for Quotiets: b b To rise quotiet to power, distribute the power to the umertor d the deomitor d multipl the powers. Emples: ) ) z z z PBCC SLC Lke Worth Mth Lb
4 . EXPONENTS OF AND ) POWER OF :" A umber or vrible rised to the st power is the umber or vrible. Emples: ) ) ) ( b) b b b) POWER OF :" A umber or vrible rised to the zero power lws equls. Whe umber or vrible is divided b itself, the result is. For emple, ; ; ; t ; t We get the sme result whe we ppl the quotiet rule: Emples: ) ) ) () ) ) j j j j + + j 9. RULE FOR NEGATIVE EXPONENTS; A egtive epoet mes tke the reciprocl of. To simplif egtive epoets, tke the reciprocl of the bse (flip) d mke the power For emple, is red "tke the reciprocl of." Sice, its reciprocl is,or : PBCC SLC Lke Worth Mth Lb
5 ) If the power i the umertor is egtive, move it to the deomitor, d mke the power Emples: ) ) ) ) b b b b) If the power i the deomitor is egtive, move it to the umertor, d mke the power Emples: ) ) p p ) ) m m m c) If the umertor d the deomitor hve egtive fctors, simplif the egtive powers first. Move egtive powers i the umertor to the deomitor; move egtive powers i the deomitor to the umertor. Emples: ) 9 ) ) i i 9 Simplif egtive epoets first, d the ppl the product d quotiet rules s eeded. ) p q q q q p p p ) Tkig the reciprocl of the iside epressio ( flippig it ) mkes the outside power ( p ) p p p p Becuse is ot rised to power, the result is egtive. p p PBCC SLC Lke Worth Mth Lb
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