Rational Exponents
If x is a nonnegative real number, then the expression
is
called the positive square root of x and is the nonnegative
number such that
is not defined in the
real numbers
 |
If no index is written, it is a square root (the
index is 2.)
|
| Remember:
|
|
If the index is even, the radicand must be positive or it
will not be
defined in the real numbers.
is not defined in the
real numbers
because
is not real
because
because
is not real
because
To simplify a radical start by writing the radicand in factored form.
Divide the exponent on the radicand by the index and remove the radical sign.
Not a real number
Rational Numbers as Exponents
Assume that:
Rational Numbers as Exponents
| Assume that:
|
In general:
|
We can work any root problem as an exponential problem by
using
rational numbers for exponents. The rules for exponents will still apply.
