5.7 rational exponents fraction exponents. radical expression and exponents by definition of radical...
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5.7 Rational 5.7 Rational ExponentsExponents
Fraction ExponentsFraction Exponents
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.
2
1
9
2 9
The Rule for Rational Exponents
46464 33
1
1
nn bb
Write in Radical form
2
1
6
1
m
a
Write in Radical form
mm
aa
2
1
66
1
Write each Radical using Rational Exponents
w
b5
Write each Radical using Rational Exponents
2
1
5
15
ww
bb
What about Negative exponents
Negative exponents make inverses.
7
1
49
149
2
12
1
What if the numerator is not 1
Evaluate
5 25
2
3232
What if the numerator is not 1
Evaluate
5 105 25
5 25
2
22
3232
What if the numerator is not 1
Evaluate
42
22
3232
2
5 105 25
5 25
2
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 mn
m
borbb
Simplify each expression
No fraction in the denominators.
3
2
7
4
7
1
x
yy
Simplify
3
1
6
1
3
6
2
16
2
16
Simplify
3
1
6
4
3
1
6
14
3
1
6
1
3
6
2
2
2
)2(
2
16
2
16
Simplify
33
1
3
1
3
2
3
1
3
2
3
1
6
4
3
1
6
14
3
1
6
1
3
6
2222
2
2
2
2
2
)2(
2
16
2
16
Simplify
6 44x
Simplify
6
4
6
16 4 44 xx
Simplify
6
4
6
12
6
4
6
16 4
2
44
x
xx
Simplify
6
4
6
2
6
4
6
12
6
4
6
16 4
2
2
44
x
x
xx
Simplify
3
2
3
1
6
4
6
2
6
4
6
12
6
4
6
16 4
22
2
44
xx
x
xx
Simplify
3 23
12
3
2
3
1
6
4
6
2
6
4
6
12
6
4
6
16 4
22
22
2
44
xx
xx
x
xx
Simplify
1
1
2
1
2
1
y
y
Simplify
1
1
1
1
2
1
2
1
2
1
2
1
y
y
y
y
Simplify
1
1
1
1
1
11
2
1
2
11
2
1
2
1
2
1
2
1
y
yyy
y
y
y
y
Simplify
1
12
1
1
1
1
1
1
2
1
1
2
1
2
11
2
1
2
1
2
1
2
1
y
yy
y
yyy
y
y
y
y
HomeworkHomework
Page 261 – 262Page 261 – 262
##21 – 61 odd, 65 21 – 61 odd, 65
Homework
Page 261
# 22 – 62 even