Download Lesson 9-3 Rational Exponents

NAME:_________________________________________________
Algebra 2: Lesson 9-3 Rational Exponents
DATE:____________
Learning Goals
1. How do we evaluate expressions with rational exponents?
2. How do we rewrite rational exponents as radicals?
DO NOW: Simplify the following expressions. Use a calculator if needed.
1. √
2. √
3. √
4.
5.
6.

Based on the questions above, how can you rewrite the expressions below?
√
Exercise #1: Rewrite each of the following using radicals, and then simplify, if possible.
1.
2.
3.
4. ( )
5.
6.
7.
8. ( )

A rational exponent does not have to be in the form . Other rational numbers, such as or
can also be used as exponents.
Let’s think about the expression . Evaluate this expression in two different ways by using the laws of
exponents. Then verify these answers with your calculator.
Rational Exponent Definition

For any rational number
we define
to be ___________ or ___________
Exercise #2: Rewrite each of the following using radicals, and then simplify, if possible.
1.
4. (
)
2.
3.
5.
6.
PRACTICE
1. Yoshiko said that
she is or is not correct.
because
is one-fourth of
. Use properties of exponents to explain why
2. Rita said that
because
, so
exponents to explain why she is or is not correct.
3. Suppose for some positive real number
that (
, and then
)
.
What is the value of ?
4. Simplify the expression
and write your answer using a positive exponent.
. Use properties of
5. Simplify the expression below and write your answer using positive exponents only.
6. Evaluate the function
7. Evaluate the function
at
( ).
for
.