Properties of Exponents
Basic skills Quiz 1 is over properties of exponents . You need to know the
following
properties:
Negative exp onents indicate a reciprocal:
Examples:
Raising to a power which is a reciprocal of an integer is the same as taking
the
corresponding root:
Note that
re presents the b -th root of a ; the number that gives a when raised to the
power b. So
because
When we have a second root, we call it a square
root and just leave out the 2 in the radical:
In general, we can raise to any rational power as a combination of a power and a root:
(Technical note: The above relation holds only if all of the above are real
numbers . We
cannot say for example that
or that
becauseis
not a real number. Just make sure you
do not al low anything inside a radical to be negative .)
Examples:
You should also know the following:
x0 =1, if x ≠ 0. ( 00 is undefined.)
x1 = x for any x.
In addition , be sure you know that in general (a + b)n
≠ an + bn. (Many students make the
mistake of thinking that they are equal.) In particular, note that
Practice Problems
Here are a few practice problems to help you prepare. Answers are on the next page.
1. Rewrite in the form
2. Rewrite in the form
3. Rewrite in the form
4. Rewrite in the form
5. Rewrite in the form
6. Rewrite in the form
7. Rewrite in the form
8. Rewrite in the form
9. Rewrite in the form
Answers:
(Note that this is not
the same as )
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