The power functions is a fundamental function with two variables that goes beyond basic math using the power of exponents. The power function has the form y equals x to the power of n, where n is a numeric constant. The power functions include the square function, the square root function, the cube function and the cube root function. A power function has two parts composed of the base number which is the x variable and the exponent of the power. The exponent is displayed above and just to the right of the base number. This function is used in quadratic equations which uses x squared. Taking the square function of x is equivalent to taking x to the power of two. Taking the cube function of x is equivalent to taking x to the power of three. These terms are founded in geometry to measure the area of a polygonal square and the volume of a solid cube. In the power functions, if the exponent is a common fraction then the base number is taken to the power of the numerator and the root of the denominator. Taking the square root of x is equivalent to taking x to the one-half power. If the exponent is a negative number then the reciprocal of the base number is taken to the absolute value of the exponent power. If the exponent is zero then the answer is always one. The power function's domain is restricted for any even root equation including the square root, the fourth root, the sixth root, etc. In these cases x is limited to being greater or equal to zero since there is no even root of a negative number defined in the set of real numbers without using imaginary numbers. The range of a power function is limited to x greater or equal to zero only when the exponent of the power or its numerator is an even integer since then the answer is always a positive number.

Square power function:
The function y = x²,
y equals x squared is x to the power of two,
or x times x.
Points: (1, 1) (2, 4) (3, 9).

Cube power function:
The function y = x³,
y equals x cubed is x to the power of three,
or x times x times x.
Points: (1, 1) (2, 8) (3, 27).

Square root function:
The function y = ,
y equals the square root of x
is the same as x to the one-half power,
or what number root is needed to be squared to be equal to x.
Points: (1, 1) (4, 2) (9, 3).

Cube root function:
y = , y equals the cube root of x
is the same as x to the one-third power
or what number is the root needed to be cubed to be equal to x.
Points: (1, 1) (8, 2) (27, 3).

Negative power function:
The function y equals x to the power of negative three
is the same as one over the quantiy of x to the power of three.
Points: (1, 1) (2, 1/8) (3, 1/27).