Math Homework. Do It Faster, Learn It Better.
Rational Exponents
POWERS OF
Definition of: (This is read asto the one-half power.) If the laws of exponents are to hold, then . Since the square ofis,is定义为 .
Example 1:
Simplify.
OTHER FRACTIONAL POWERS
Definition ofis defined to be, since its cube is.
Definition ofis defined to be, sinceis.
Definition of: Using the Power of a Power Law of Exponents in either of two ways:
Therefore,is defined to be either of the equivalent expressionsor.
The definition of any rational exponent is:
Ifandare integers,andis a positive real number, then
.
Example 2:
Simplify.
CUBE ROOTS AND OTHER RADICALS
Fractional exponents can also be written as radicals: