Warm Up
Simplify each expression.
1.
4.
√36
2.
4
√1
5.
5
√0
3.
5
6.
√100,000
3
√64
3
– √27
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Algebra/Lesson 6-2: Rational Exponents
Objectives:

Evaluate and simplify expressions containing rational exponents.
Recall that the radical symbol
which root to take. For example
is used to indicate roots. The index is the small number to the left of the radical symbol that tells
represents a cubic root. Since 23 = 222 = 8,
Another way to write nth roots is by using fractional exponents. For example, for b >1, suppose
1
𝟏
Additional Example 1: Simplifying 𝒃𝒏
Simplify each expression.
A.
1
3433
B.
1
1
325 + 92
C.I.O.-Example 1:
Simplify each expression.
a.
1
814
b.
1
1
1212 + 2564
2
A fractional exponent can have a numerator other than 1, as in the expression 𝑏 3 . You can write the exponent as a product in two
different ways.
Example 2: Simplify each expression.
2
C.I.O.-Example 2: Simplify each expression.
a.
3
164
b.
3
15
c.
4
273
Additional Example 3: Application
3
𝑠 2
Given a cube with surface area S, the volume V of the cube can be found by using the formula 𝑉 = ( ) .
6
Find the volume of a cube with surface area 54 m2.
C.I.O.-Example 3:
3
The approximate number of Calories C that an animal needs each day is given by = 72𝑚4 , where m is the animal’s mass in
kilograms. Find the number of Calories that an 81 kg panda needs each day.
Remember that
always indicates a nonnegative square root. When you simplify variable expressions that contain , such as
the answer cannot be negative. But x may be negative. Therefore you simplify
as |x| to ensure the answer is nonnegative.
3
When n is even, you must simplify
to |x|, because you do not know whether x is positive or negative. When n is odd, simplify
to x.
Example 4: Simplify. All variables represent nonnegative numbers.
A.
B.
C.I.O.-Example 4: Simplify. All variables represent nonnegative numbers.
a.
b.
Lesson Quiz: Part I
Simplify each expression.
1.
2.
3.
4.
4
Lesson Quiz: Part II
5. In an experiment, the approximate population P of a bacteria colony is given by
of the experiment. Find the population of the colony on the 8th day.
, where t is the number of days since start
Simplify. All variables represent nonnegative numbers.
6.
7.
p. 401: 31-59 odd, 63-79 odd
5