Example of Even Exponents

There is no real number that multiplied by itself or squared gives a negative number, from which it follows that always that the exponent is even, the result is positive so we cannot find square roots (index 2) of numbers negatives. What is the cube root of -8, is equivalent to asking what is the number that cubed gives us -8 Answer: -2
Because (-2) = (-2) (-2) (-2) = - 8
And the cube root of -64 (-4)
(-4)³ =(-4)(-4)(-4) = -64 

From all the previous examples we conclude that:

From a positive number two real roots are obtained or only one, depending on whether n is even or odd respectively and that from a negative number a negative or no root is obtained depending on whether n is odd or even respectively.

EXAMPLES:

a) Let 64 AND P, the square roots (even n) will be 8 and -8 because 8² = (-8)² = 64.

b) Let 8 E P, the cube root (odd n) is 2 because it is the only real number that cubed 8.

c) -27AND P, the only cube root is -3 because (-3)³ = -27; 3³ = -27.

d) -64AND P, the root, square does not exist in the set of real numbers (even n).