Radical Expressions And Rational Exponents Worksheet Page 4
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1
2
3
45
E X A M P L E
Simplifying Expressions with Rational Exponents
Simplify each expression.
_
1
_
_
_
3
2
3
8
· 25
A
5
5
B
25
_
2
3 _
+ 2 _
3
8
5
5
25
Product of Powers
1 _
- 2 _
3
3
8
1
Quotient of Powers
25
Simplify.
- 1 _
3
8
Simplify.
25
Evaluate the power.
1 _
Negative Exponent
Check Enter the expression in a
1 _
Property
graphing calculator.
3
8
1 _
Evaluate the power.
2
Check Enter the expression in a
graphing calculator.
Simplify each expression.
9 _
3 _
1 _
- 1 _
4
5c. 5
(
)
_
· 36
-8
8
8
5a. 36
5b.
3
1 _
4
5
E X A M P L E
6
Music Application
E string
Frets are small metal bars positioned across the
Frets
neck of a guitar so that the guitar can produce the
notes of a specific scale.
To find the distance a fret should be placed from
64 cm
the bridge, multiply the length of the string by
_
n
-
12
2
, where n is the number of notes higher
than the string’s root note. Where should a fret be
Bridge
placed to produce a G note on the E string
(3 notes higher)?
(
)
(
)
- n _
- 3 _
= 64
12
12
64
2
2
Use 64 cm for the length
of the string, and
)
(
substitute 3 for n.
- 1 _
= 64
4
2
Simplify.
)
(
1 _
= 64
Negative Exponent Property
1 _
4
2
= 64
_
Simplify.
1 _
4
2
≈ 53.82
Use a calculator.
The fret should be placed about 53.82 cm from the bridge.
6. Where should a fret be placed to produce the E note that is one
octave higher on the E string (12 notes higher)?
8- 6 Radical Expressions and Radical Exponents
613
613
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