** 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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