Cool math Algebra Help Lessons: Radicals - Fractional Exponents (rational exponents)

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Coolmath Algebra
Radicals lesson 7 - Fractional (rational) Exponents (page 1 of 4)
---- This algebra lesson explains fractional (rational) exponents.

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Don't get all freaked out about these -- it's just a different notation for what you've already been doing.

	can be written as
	can be written as

* Remember that is really ... We just assume the 2.

Not that bad, is it?

Here's the general rule:

the nth root of a = a^(1/n)

This notation has some advantages because it will help you understand some things better.

Check it out:

sqrt(5) * sqrt(5) = ( 5^(1/2) ) * ( 5^(1/2) ) = 5^( 1/2 + 1/2 ) = 5^1 = 5

Now, we can show why this rule works:

( the nth root of a ) * ( the nth root of b ) = the nth root of ab

( the nth root of a ) * ( the nth root of b ) = ( a^(1/n) ) * ( b^(1/n) ) = ( ab )^(1/n) = the nth root of ab

Continued on the next page

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