rational (fraction) exponents please read as well as take notes & complete the problems followed...
DESCRIPTION
How would we simplify this expression? What does the fraction exponent do to the number? The number can be written as a Radical expression, with an index of the denominator.TRANSCRIPT
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Rational (fraction) Rational (fraction) ExponentsExponents
Please READ as well as take Please READ as well as take notes & complete the notes & complete the
problems followed in these problems followed in these slides.slides.
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Radical expression and Exponents
By definition of Radical Expression.
The index of the Radical is 3.
51251255 33 so
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How would we simplify this expression?
What does the fraction exponent do to the number?
The number can be written as a Radical expression, with an index of the denominator.
21
9
2 9
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The Rule for Rational Exponents
46464 331
1
nn bb
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Write in Radical form
21
61
m
a
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Write in Radical form
mm
aa
21
661
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Write each Radical using Rational Exponents
w
b5
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Write each Radical using Rational Exponents
21
51
5
ww
bb
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What about Negative exponents
Negative exponents make inverses.
71
49
14921
21
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What if the numerator is not 1
Evaluate5 25
2
3232
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What if the numerator is not 1
Evaluate
5 105 25
5 252
22
3232
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What if the numerator is not 1
Evaluate
42
22
3232
2
5 105 25
5 252
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For any nonzero real number b, and integer m and n
Make sure the Radical express is real, no b<0 when n is even.
mnn mnm
borbb
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Simplify each expression
No fraction in the denominators.
32
74
71
x
yy
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Simplify
31
61
3
6
2
16216
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Simplify
31
64
31
61
4
31
61
3
6
2
2
2
)2(
2
16216
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Simplify
331
31
32
31
32
31
64
31
61
4
31
61
3
6
22222
2
2
2
2
)2(
2
16216
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Simplify
6 44x
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Simplify
64
61
6 4 44 xx
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Simplify
64
61
2
64
61
6 4
2
44
x
xx
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Simplify
64
62
64
61
2
64
61
6 4
2
2
44
x
x
xx
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Simplify
32
31
64
62
64
61
2
64
61
6 4
22
2
44
xx
x
xx
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Simplify
3 231
2
32
31
64
62
64
61
2
64
61
6 4
22
22
2
44
xx
xx
x
xx