Algebra 2 unit 6.4
28
Holt Algebra 1 UNIT 6.4 RATIONAL UNIT 6.4 RATIONAL EXPONENTS EXPONENTS
-
Upload
mark-ryder -
Category
Education
-
view
102 -
download
3
Transcript of Algebra 2 unit 6.4
Holt Algebra 1
UNIT 6.4 RATIONALUNIT 6.4 RATIONALEXPONENTSEXPONENTS
Warm UpSimplify each expression.
1.
2.
3.
4.
5.
6.
6
0
4
1
10
–3
Evaluate and simplify expressions containing rational exponents.
Objective
index
Vocabulary
Recall that the radical symbol is used to indicate roots. The index is the small number to the left of the radical symbol that tells which root to take. For example represents a cubic root. Since 23 = 222 = 8,
Another way to write nth roots is by using fractional exponents. For example, for b >1, suppose
1 = 2k
So for all b > 1,
Square both sides.
Power of a Power Property
If bm = bn, then m = n.
Divide both sides by 2.
b1 = b2k
When b = 0,
When b = 1,
Helpful Hint
Additional Example 1: Simplifying b1n
Simplify each expression.
A.
= 7
b1nUse the definition of .
B.
b1nUse the definition of .
= 2 + 3 = 5
Check It Out! Example 1
Simplify each expression.
a.
= 3
b.
= 11 + 4
= 15
b1nUse the definition of .
b1nUse the definition of .
A fractional exponent can have a numerator other than 1, as in the expression . You can write the exponent as a product in two different ways.
Power of a PowerProperty
Definition of
Additional Example 2: Simplifying Expressions with Fractional Exponents
Simplify each expression.
A. B.
Definition of
= 243 = 25
Check It Out! Example 2
Simplify each expression.
a.
= 8
b.
= 1
Definition of
= (1)3
Check It Out! Example 2
Simplify each expression.
= 81
Definition of
c.
Additional Example 3: ApplicationGiven a cube with surface area S, the volume V of the cube can be found by using the formula
Find the volume of a cube with surface area 54 m2.
Substitute 54 for s.
Simplify inside the parentheses.
Definition of
The volume of the cube is 27 m3.
Check It Out! Example 3 The approximate number of Calories C that an 2
animal needs each day is given by , where m is the animal’s mass in kilograms. Find the number of Calories that an 81 kg panda needs each day.
= 7227 = 1944
The panda needs 1944 Calories per day to maintain health.
Substitute 81 for m.
Definition of
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.
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.
When you are told that all variables represent nonnegative numbers, you do not need to use absolute values in your answer.
Helpful Hint
Additional Example 4A: Properties of Exponents to Simplify Expressions
Simplify. All variables represent nonnegative numbers.
Power of a Product PropertyPower of a Power Property
Simplify exponents.
•
Definition of
Additional Example 4B: Properties of Exponents to Simplify Expressions
Simplify. All variables represent nonnegative numbers.
Power of a Product Property
Product of Powers Property
Simplify exponents.
• •
Check It Out! Example 4a
Simplify. All variables represent nonnegative numbers.
Power of a Product Property
Simplify exponents.
Definition of
Check It Out! Example 4a
Simplify. All variables represent nonnegative numbers.
Power of a Product Property
Simplify exponents.
Definition of
Check It Out! Example 4b
Simplify. All variables represent nonnegative numbers.
Power of a Product Property and
Simplify.
= xy
Lesson Quiz: Part I
Simplify each expression.
1.
2.
3.
4.
9
2
128
729
In an experiment, the approximate population P of a bacteria colony is given by
, where t is the number of days sincestart of the experiment. Find the population of the colony on the 8th day.
5.
480
Simplify. All variables represent nonnegative numbers.
6.
7.
Lesson Quiz: Part II
All rights belong to their respective owners.Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for "fair use" for purposes such as criticism, comment, news reporting, TEACHING, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, EDUCATIONAL or personal use tips the balance in favor of fair use.
