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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.