Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and...
-
Upload
emery-wood -
Category
Documents
-
view
225 -
download
0
Transcript of Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and...
![Page 1: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/1.jpg)
Powers, Roots, & Radicals
OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.
![Page 2: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/2.jpg)
Rational Numbers: can be written as a ratio.
Rational Expression:
Rational Function:
2 5 4 11, , , , 0.25, 0.333...,
3 21 1 9etc
3 2
2
8 7
3 5 14
x x xf x
x x
6 5,
1
x
x x
![Page 3: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/3.jpg)
n a Radicand
Index
1 nn a a1 4 4 481 81 3 3 3 3 3
1mmm n n na a a
333 2 1 2 39 9 9 3 27
![Page 4: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/4.jpg)
Simplest Form – properties of radicals have been applied, perfect nth powers have been removed, and any denominators have been rationalized.
Like Radicals – radical expressions that have the same index and the same radicand.
![Page 5: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/5.jpg)
Example: 31/2 . 33/2
![Page 6: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/6.jpg)
Example: (43/2)2
![Page 7: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/7.jpg)
Example: (9 . 4)1/2
![Page 8: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/8.jpg)
Example: 25 -1/2
1, 0
ma
a
![Page 9: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/9.jpg)
Example:
0m
n
aa
a
5/2
1/2
6
6
![Page 10: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/10.jpg)
Example
, 0m m
m
a ab
b b
1/38
27
Property:
![Page 11: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/11.jpg)
Use the properties of rational exponents to simplify the expressions. a.
b.
c.
1/2 1/45 5
21/2 1/38 5
1/44 42 3
![Page 12: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/12.jpg)
1. 27 12 Can only combine like terms! Goal is to simplify each term to see if “life terms” result. “Like radicals” have the same index and the same radicand.
332. 16 2
![Page 13: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/13.jpg)
63
8 4 104
4
48
1. 250
2. 64
3.
y
a b c
x
y
![Page 14: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/14.jpg)
3 35 22. 3 5 40x x x
651. 6 7y y
![Page 15: Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697c0141a28abf838ccd26d/html5/thumbnails/15.jpg)
Read Section 7.2 Pgs. 411-14: 24-81 (x3)