ALGEBRA - solved problems
  Radicals (roots) and/or exponentiation with fractional (rational) exponent
     Rules and properties of radicals
67.    Find given roots or radicals.
Solutions: a)   since  33 = 27.
b)   since  (-3)3 = (-3)(-3)(-3) = - 27.
c)   since  (-2)5 = (-2)(-2)(-2)(-2)(-2) = -32.
The odd root of any real number exists.
68.    Find given roots.
Solutions: a)   since  42 = 16 and  4 > 0,   [recall that  ( 4)2 = 16].
  b)   since  34 = 81 and  3 > 0,   [recall that  ( 3)4 = 81].
The even root of a nonnegative real number exists. Note that the even root is defined to be a nonnegative number. 
The even root of a negative real number does not exist as a real number.
For example,   do not exist as real numbers, but they do exist as complex numbers.
Rules and properties of radicals and/or fractional exponents
If m, n and p are natural numbers (n >1) and if  a and b are nonnegative real numbers, then
Properties Examples
   
   
   
   
   
   
   
   
Simplifying radical expressions
69.    Simplify radical expressions.
Solutions:
 
  Operations on radical expressions
Adding, subtracting and multiplying radicals
70.    Solve given radical expressions.
Solutions:
 
71.    Solve given radical expressions.
Solutions:
                 
72.    Solve given radical expressions.
Solutions:
73.    Solve given radical expressions.
Solutions:
 
74.    Solve given radical expressions.
Solutions:
 
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