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Want to watch animated videos and solve interactive exercises of examples of solving powers with variables?
A power:
consists of a base and an exponent . The base is the number that is to be multiplied with itself times.
Rule
Note!
Pay special attention to the fact that . This is called the square root of . It then follows that . This is called the th root of .
If is an even number, you get an even root. Some examples include
In the same way, you get odd roots when is an odd number. They look like this:
The difference between even and odd roots is that even roots are only defined for . In odd roots, can be either positive or negative.
Note! You can not take the even root of a negative number. is undefined!
Example 1
Write as simply as possible
Example 2
Write as simply as possible
Example 3
Write as simply as possible
Example 4
Write as simply as possible
Note! When you have a negative exponent, it’s usually best to write the power as a fraction. The reason to do this is that in general, positive exponents are much easier to deal with than negative ones.