subject: Rational Exponent [print this page] Introduction to rational exponent form: Introduction to rational exponent form:
The rational exponent is the form of exponent function in which it is also called as the algebaric expression of the exponent form. Let u be the real number, algebraic expression or variable, and n is an integer greater than one, Then the function is
'u^(1/n) = nsqrtu'
If mis a positive integer, 'm/n' is in the reduced form, and all the roots are the real numbers, then
'u^(m/n) = (u^(1/n))^m = ((nsqrtu))^m'
The numerator of the rational exponent is the power to which the base is raised, and the denominator is the root to be taken. The fraction ' m/n' is to be in reduced form. For the rational exponent of function is given. Here we are going to see about the radical exponent form and the example problems in it.
Representations of Rational Exponent Form :
Function 'a^(1/n)' :
The rational exponent 'a^(1/n) = nsqrta'
If n is odd then,
If a is positive, then the 'a^(1/n)' is positive.
If a is negative, then the 'a^(1/n)' is negative.
If a is zero, then the 'a^(1/n)' is also zero
If n is even then,
If a is positive, then the 'a^(1/n)' is positive.
If a is negative, then the 'a^(1/n)' is not a real number.
If a is zero, then the 'a^(1/n)' is also zero
Rational Expression:
'x^(1/m) = msqrt(x)' it is a m root of x
Relation between expression and rational:
'"(x^(1/m))^m' is the relation between the expression and rational .
Rational Exponent of Product:
'"msqrt(axxb) = (axxb)^(1/m) = msqrta xx msqrtb = a^(1/m) xx '
