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12 Nov 2019
CHAPTER O INQUIRY-BASED LEARNING PROIECT Understanding Rules through Patems and Examples In this chapter, you reviewed many definitions, ules, and properties from youtr previous algebra casses It can be a lot to remember, and sometimes it's eany to misremember something Observing pattems can help you see that nules are not arbitrary, rather they make sense in the context of other mathematics you already know And by looking at eramples, you can test whether you've comectly remembered a nule. You will esplore both of those strategies here 1. In this part, you will observe pattems to try to disoover some of the nules for exponents given in this chapter a. For instance, to discover a rule for zero as an exponent, first complete the neat four steps As the power decreases by one at each step, what patten do you notice? Extend this pattem to find the neat step. Now complete this nule Let a be any nonzero whole umber Then af Notice in the statement of the above rule, the base a is required to be nonzera. To see why, consider these two pattems: 4P- 1 3-1 22-1 19-1 0-0 o'-0 According to this pattem According to tha pattem, 0° should be oP should be_ Since these two patterns are not consistent, we say that O' is undefined. b. Look again at the pattern in part (a) that shows why a ought to be defiened as 1, for nonzero a Wite the next several steps after a, following the same pattern. To be consistent with the patem, how should we Let a be any nonzero whole number. deline a 7 Then Observing patterns can be helphul for making sense of nules, but an equaly useful tool is looking at examples. Trying several examples can help you better understand given rules, or decide whether an equation is in fact a rule, as you wil see in the next several parts.
CHAPTER O INQUIRY-BASED LEARNING PROIECT Understanding Rules through Patems and Examples In this chapter, you reviewed many definitions, ules, and properties from youtr previous algebra casses It can be a lot to remember, and sometimes it's eany to misremember something Observing pattems can help you see that nules are not arbitrary, rather they make sense in the context of other mathematics you already know And by looking at eramples, you can test whether you've comectly remembered a nule. You will esplore both of those strategies here 1. In this part, you will observe pattems to try to disoover some of the nules for exponents given in this chapter a. For instance, to discover a rule for zero as an exponent, first complete the neat four steps As the power decreases by one at each step, what patten do you notice? Extend this pattem to find the neat step. Now complete this nule Let a be any nonzero whole umber Then af Notice in the statement of the above rule, the base a is required to be nonzera. To see why, consider these two pattems: 4P- 1 3-1 22-1 19-1 0-0 o'-0 According to this pattem According to tha pattem, 0° should be oP should be_ Since these two patterns are not consistent, we say that O' is undefined. b. Look again at the pattern in part (a) that shows why a ought to be defiened as 1, for nonzero a Wite the next several steps after a, following the same pattern. To be consistent with the patem, how should we Let a be any nonzero whole number. deline a 7 Then Observing patterns can be helphul for making sense of nules, but an equaly useful tool is looking at examples. Trying several examples can help you better understand given rules, or decide whether an equation is in fact a rule, as you wil see in the next several parts.
Deanna HettingerLv2
17 Feb 2019