Page 66 - ArithBook5thEd ~ BCC

It remains true that 0 can be the dividend.

Example 69. 0÷(−12) = 0. Note that this can be restated in terms of multiplicationas 0×(−12) = 0.
We summarize the properties of 0 with respect to division.

For a nonzero signed number N

• 0 ÷ N =0

• N ÷ 0is undefined.
0 ÷ 0is alsoundefined.

2.6.1 Exercises

Perform the divisions, or state that they are undefined.

1. (−24) ÷ (−8)

2. (−24) ÷ 8

3. 66 ÷ 0
4. 30 ÷ (−6)

5. (−30) ÷ 6

6. 0 ÷ (−1000)

7. 50 ÷ (−4)

8. −95 ÷ 0

2.7 Powers of Signed Numbers

Since exponents indicate repeated multiplication, there is no problem applying exponents to signed
numbers.

4
3
(−4) =(−4)(−4)(−4) = −64 and (−2) =(−2)(−2)(−2)(−2) = 16.
3
4
Example 70. Evaluate (−5) ,and (−5) .
Solution.
3
(−5) =(−5)(−5)(−5) = (25)(−5) = −125.
4
(−5) =(−5)(−5)(−5)(−5) = (25)(25) = 625.

Notice that every pair of negative factors has a positive product, by the rules for multiplying signed
numbers with the same sign. It follows that

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