MATH 10 Module 4 (Rational Exponents and Radical Expressions)
Unit: Radical Functions 7-4: Rational Exponents
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Transcript of Unit: Radical Functions 7-4: Rational Exponents
Essential Question:
Explain the meaning of using radical expressions
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Another way to write a radical expression is to use a radical exponent.
Examples:
Radical Form
Exponent Form
=
=
=
253 274 16
122513271416
Rational Exponents can be simplified just like their radical counterparts.
Examples:
13 3125 125
5
1 12 25 5 5 5
5
1 13 3 3 3
3
10 100 10 100
1000
10
YOUR TURNSimplify
1416
1 12 22 21 12 22 8
4 16 2 1 12 22 2
1 12 22 8 16 4
Note that: 1) Like variables, you can add exponents when the base is the same 2) You can multiply bases when the exponent is the same
A rational exponent may have a numerator other than 1. The property (am)n = amn shows how to rewrite such an expression.
or
Basically, the numerator is the power a number is being raised to. The denominator is the root a number is being taken to.
13 1 22 23 3 325 25 25 25
3 1 12 2 2
3 3325 25 25 25
We can convert between the two forms Write the exponential expression in radical form:
Write the radical expressions in exponential form:
35
35 3 5x x or x
52
52
2.555
1 1 1y y or
y y y
323a a
25
25 b b
YOUR TURN Write the exponential expression in radical form:
Write the radical expressions in exponential form:
0.4z38y
25
25 2 5z z or z
38
338 8
1 1 1or
y y y
3 2x
3y23x
32y
Simplifying Numbers with Radical ExponentsAll the properties of integer exponents also
apply to rational exponents.See page 381 in your books for a summary.Examples:
35
35
3
32 32
2
8
72
72
3.5
7 7
14 4
4
1 1
241
128
YOUR TURN
3225
3532
45( 32)
32
3 3
1 1 1 1
5 12525 25
3 35 32 2 8
4 45 32 ( 2) 16
Writing in simplest form:
3 3 34 4 4
34
88
6 63
4
6 63
6
16 16
1 1
16 16
1 1
2 8
8
y y
y y
y y
y
YOUR TURNSimplify
13158x
1 13 3
13
15
5
53
5 5
8
1
81 1
81 1 1
2 2
x
x
x
x x
AssignmentPage 388 - 3891 – 25 & 31 – 49Odd problemsShow work