Rational (fraction) Exponents Please READ as well as take notes & complete the problems followed...
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Transcript of Rational (fraction) Exponents Please READ as well as take notes & complete the problems followed...
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.
Radical expression and Exponents
By definition of Radical Expression.
The index of the Radical is 3.
51251255 33 so
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
The Rule for Rational Exponents
46464 331
1
nn bb
Write in Radical form
21
61
m
a
Write in Radical form
mm
aa
21
661
Write each Radical using Rational Exponents
w
b5
Write each Radical using Rational Exponents
21
51
5
ww
bb
What about Negative exponents
Negative exponents make inverses.
71
49
14921
21
What if the numerator is not 1
Evaluate5 25
2
3232
What if the numerator is not 1
Evaluate
5 105 25
5 252
22
3232
What if the numerator is not 1
Evaluate
42
22
3232
2
5 105 25
5 252
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
Simplify each expression
No fraction in the denominators.
32
74
71
x
yy
Simplify
31
61
3
6
2
16216
Simplify
31
64
31
61
4
31
61
3
6
2
2
2
)2(
2
16216
Simplify
331
31
32
31
32
31
64
31
61
4
31
61
3
6
22222
2
2
2
2
)2(
2
16216
Simplify
6 44x
Simplify
64
61
6 4 44 xx
Simplify
64
61
2
64
61
6 4
2
44
x
xx
Simplify
64
62
64
61
2
64
61
6 4
2
2
44
x
x
xx
Simplify
32
31
64
62
64
61
2
64
61
6 4
22
2
44
xx
x
xx
Simplify
3 231
2
32
31
64
62
64
61
2
64
61
6 4
22
22
2
44
xx
xx
x
xx