SOLUTION: Use rational exponents to simplify. Write the answer in radical notation, if possible. exponent of 12 SQRT (a^10)

Question 352392: Use rational exponents to simplify. Write the answer in radical notation, if possible.

exponent of 12 SQRT (a^10)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
For this problem you need to understand:

The relationship between radicals and rational/fractional exponents:
Square roots are "second roots". IOW: is the same as .

So written with rational exponents would be:

Using the rule for exponents, , we can simplify the "a" part of the above:

which simplifies to

There is only one thing left. All square roots are supposed to be positive or zero, including . And 12 times a positive number or zero, like 12sqrt(a^10), will be positive or zero. However, our answer at this point is not necessarily positive or zero. In fact, if "a" is negative then will be negative, too. Since "a" could be negative (there's no reason it can't be), we cannot use for the answer. We must somehow ensure that our answer must be positive or zero. There are a variety of expressions we could use. Probably the preferred one is found as follows:

This expression will always be positive or zero no matter what "a" is.
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