Define 0 and negative exponents

Define 0 and negative exponents


 So far we have discussed only positive exponents. Now we define 0 as an exponent. Suppose

we multiply 42by 40. By the product rule, extended to whole numbers,

42 . 40 = 42+0 = 42.

For the product rule to hold true, 40must equal 1, and so we define a0this

way for any nonzero real number a.

Zero Exponent

If a is any nonzero real number, then

a0= 1.

The expression 00is undefined.*


Negative Exponent

For any natural number n and any nonzero real number a,

a-n = 1/an.


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