1. Properties of Rational Exponents
Section 7.2

2. Review of Properties of Exponents
am * an = am+n
(am)n = amn
(ab)m = ambm
a-m=
= am-n =
These all work for fraction exponents as well as integer exponents.

3. Ex: Simplify. (no decimal answers)
(43 * 23)-1/3
= (43)-1/3 * (23)-1/3
= 4-1 * 2-1
= ¼ * ½
= 1/8 d.
= = =
61/2 * 61/3
= 61/2 + 1/3
= 63/6 + 2/6
= 65/6
b. (271/3 * 61/4)2
= (271/3)2 * (61/4)2
= (3)2 * 62/4
= 9 * 61/2
** All of these examples were in rational exponent form to begin with, so the answers should be in the same form!

4. Ex: Write the expression in simplest form.
Ex: Simplify. =
= = 5
= = 2
Ex: Write the expression in simplest form.
= = =
= =
Can’t have a radical in the denominator!
** If the problem is in radical form to begin with, the answer should be in radical form as well.

5. Ex: Perform the indicated operation
5(43/4) – 3(43/4)
= 2(43/4) b. = c. =
If the original problem is in radical form,
the answer should be in radical form as well.
If the problem is in rational exponent form, the answer should be in rational exponent form.

6. More Examples a. b. c. d.

7. Ex: Simplify the Expression. Assume all variables are positive.
(16g4h2)1/2
= 161/2g4/2h2/2
= 4g2h c. d.

8. Ex: Write the expression in simplest form
Ex: Write the expression in simplest form. Assume all variables are positive. a. b.
No radicals in denominator! c.
** Remember, solutions must be in the same form as the original problem (radical form or rational exponent form)!!

9. d.
Can’t have a radical in denominator!!

10. Ex: Perform the indicated operation. Assume all variables are positive.

11. e.