It is a common practice to use patterns involving exponents to show why *b*^0 = 1 and also why negative exponents such as *b*^-*a* give us fractions….

Can we use this same type of thinking to help us understand **why **Let’s first take a look at

To continue the pattern established in ** Figure 1**, 1 times some unknown factor,

*b*, will have to give us a missing number,

*k*, such that when we multiply

*k*by the same factor

*b*we must get 3.

Therefore, since

we have

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