1. Exponents and Roots
1. Exponentiation
   Multiplying a number several times, such as , is called exponentiation of . In , is called the base of the exponent, and is called the exponent.
   
   
2. -th Root
   For a real number and a natural number , a number that, when raised to the power , equals , i.e., a solution to the equation , is called the -th root of . The square root, cube root, and higher roots of are collectively referred to as the roots of .
   
   
3. Relationship between the -th root of and ( -th Root of )

4. is even		0	Does not exist
   is odd		0

   a > 0 a=0 a < 0 n is even root(n)(a),-root(n)(a) 0 Does not exist n is odd root(n)(a) 0 root(n)(a)
5. Properties of Roots
   When , , and are integers greater than or equal to 2:
5. (where is a positive integer)


2. Extension of Exponents
1. When the exponent is 0 or a negative integer
   For and a positive integer:
   
2. When the exponent is a rational number
   For and integers and (where ):
   
3. Laws of Exponents
   When , , and are real numbers: