Properties of Exponents

Basic skills Quiz 1 is over properties of exponents . You need to know the following
properties:

Negative Exponents

Negative exp onents indicate a reciprocal:

Examples:

Fractional Exponents

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:

Miscellaneous Properties

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 )