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HW: Textbook Pg. 406 #1-13 odd, 19-33 odd, 37-41 odd, 45-51 odd, 57-59 odd
Algebra II Pre AP
Notes 9.4 Simplifying Radicals & Rational Exponents
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Date: ______________ Per: ________
Review & Extend – Simplifying any Radical (Remember to use absolute value only when necessary.)
1.
4.
3
7.
50x6 y 7
2.
9 x2  6 x  1
3.
8x6 y10 z17
5. 4 162x8 y12 z 23
6.
1
4
2x
8.
1
3
9.
4x 2
3
2 x 3  32 x5
3
24x 21 y13
128 x 6 y 2
3x 2 y 7
10.
Key Concept: If the nth root of a is a real number, m is an integer, and m/n is in lowest terms, then
m
1
an  n a
and
a n  n am 
 a
n
m
Write in simplest exponential form using rational exponents.
11.
 b
5
3
 2x 2 yz 3
12. 6 a 5
13.
15. y 3.5
16. 6x 5 y 5 z
5
Write in simplest radical form.
15
14. x 4
11
3
4
48 z 4
9 y3 x
Properties of Rational Exponents: Let m and n represent rational numbers. Assume that no denominator equals 0.
Apply the rules of exponents to simplify, and express in exponential form.
(Remember exponents can be any real number, thus all the rules apply to the examples below.)
17. 216
1
3
1
4
18. 5  125
1
2
19.
x x
3
1 12
20.
16
2
3
 321/ 3 
21.  1/ 3 
 2 
1
46
2
Apply the rules of exponents to simplify, then express in radical form and simplify, if necessary.
1
6
22. 32  8
1
4
2
15
2
6
1
6
*23. 243 x  9 x
8
12
24.
x
x
2
3
5
6
Write in simplest radical form. (Remember to use absolute value only when necessary.)
 When a radical expression cannot be simplified in its current form:
o Rewrite in exponential form
o Apply the rules of exponents
o Then rewrite in terms of the same radical
o Simplify the resulting radical expression
o Reduce indices, if needed
25.
4
9
26.
28.
4
36 x 4 y 2  5 3 6 x 2 y
29.
6
324x 4 y 8 z 2
14 xy
42 8 xy
3
2
27.
30.
3
8 x  6 x 2  5 9 x3
5 3
x
*Note – Whenever the final answer is to be expressed in radical form, there is a chance absolute value signs will be needed. Refer to the original
problem to determine if they might be necessary and then evaluate your final expression.