1. Simplify expressions in exponential or radical form.
5.7 Rational Exponents
Objectives:
Write expressions with rational exponents in radical form, and vice-versa.
Simplify expressions in exponential or radical form.

2. Rational Exponents
For any real number b and for any positive integer n, except when b<0
and n is even.
(Any number raised to the ½ power is the same as the square root of the number etc.)
Examples:

3. Rational Exponents
For any nonzero real number b and any integers m and n, with n>1,
except when
b<0 and n is even.
Examples:

4. Simplifying Rational Exponents
To be considered simplified, the expression must meet the following conditions:
No negative exponents.
No fractional exponents in the denominator.
Not a complex fraction.
The index of any remaining radical is the least number possible.

5. Examples:
Write in radical form.
Write using rational exponents.

6. Writing Answers Should your answer be written with a
rational exponent or as a radical? It depends on how the problem was written. If it starts out as a rational exponent, the answer should also be a rational exponent. If it starts out as a radical, the answer should be expressed as a radical.

7. Examples
Simplify

8. More Examples
Simplify

9. Example
Simplify

10. Rationalizing with Binomials
Rationalize:

11. Homework
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