|
|
The Purplemath Forums |
Exponents and Negative Numbers (page 4 of 4) Sections: Introduction, Adding and subtracting, Multiplying and dividing, Negatives and exponents Now you can move on to exponents, using the cancelation-of-minus-signs property of multiplication. For instance, (3)2 = (3)(3) = 9. In the same way:
(–3)2 = (–3)(–3) = (+3)(+3) = 9 Note the difference between the above exercise and the following:
–32 = –(3)(3) = (–1)(9) = –9 In the second exercise, the square (the "to the power 2") was only on the 3; it was not on the minus sign. Those parentheses make all the difference in the world! Be careful with them, especially when you are entering expressions into software. Different software may treat the same expression very differently, as one researcher has demonstrated very thoroughly.
(–3)3
= (–3)(–3)(–3)
(–3)4
= (–3)(–3)(–3)(–3)
(–3)5
= (–3)(–3)(–3)(–3)(–3) Note the pattern: A negative number taken to an even power gives a positive result (because the pairs of negatives cancel), and a negative number taken to an odd power gives a negative result (because, after canceling, there will be one minus sign left over). So if they give you an exercise containing something slightly ridiculous like (–1)1001, you know that the answer will either be +1 or –1, and, since 1001 is odd, then the answer must be –1. Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved You can also do negatives with roots, but only if
you're careful. You can do
...because 42 = 16. But what
about
...because (–2)3 = –8. For the same reason, you can take any odd root (third root, fifth root, seventh root, etc.) of a negative number. << Previous Top | 1 | 2 | 3 | 4 | Return to Index
|
|
|
|
Copyright © 1999-2012 Elizabeth Stapel | About | Terms of Use |
|
|
|
|
|
|
, because
there is a number that squares to 16. That is,
? Can you square anything
and have it come up negative? 
