FRACTIONAL EXPONENTS AND RADICALS

1. = 3  This symbol tells us to look for a number which when multiplied by itself 3 times will equal 27.  We say verbally that we want the cube root of 27. The 3 is called the index and the 27 is the radicand.  The symbol  is called the radical sign.

What does  =  answer

2. = 2   The index 4 tells us that we are looking for the fourth root of 16. Meaning that we are looking for a number which when multiplied by itself 4 times equal 16. 2 is the answer because 2x2x2x2 =16.

3.  = 4  This is read the square root of 16 is 4. By tradition we do not write the index 2 so the problem will look like this = 4       

 =  answer

Radicals can be written with fractional exponents instead of radical signs. So  can be written 16^1/4 ,     can be written 8^1/3     The answers will be the same.

All the rules that apply to whole number exponents 

must also apply to fractional exponents.

So  (t^1/5 )(t^2/5 ) = t^{1/5 + 2/5} = t^3/5

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