7.2 1
7.2 Rational Exponents Rational Exponents Exponential Expressions – Variables in Bases Rational Exponents with Numerators > 1 Negative Rational Exponents Applying Exponent Rules Simplifying Radical Expressions
7.2 2
Rational (Fractional) Exponents Rational Exponents can be used to express
and manipulate factors containing radicals
21
51
31
99776464 53
7.2 3
Recall the Rules for Integer Exponents
5555 exponents, of rule theUsing
555555 expression that theseecan We
122
122
1
2
835 xxx 1535 )( aa 216372 )( yxyx
6
10
3
5 2
ba
ba
10 y3
13
xx 2
4
6
xxx 33
5
3
3
5
ab
ba
7.2 4
Practice
71
31
21
)4(4)3(3)44(44 723 2 zzyyxx
42)2()2(1616 244 21
21
21
Express using rational exponents:
Simplify using rational exponents:
2
3
2
3
8
27
8
273
1
31 3
3
7.2 5
Expressions with Variable BasesAssume that all variables are unrestricted and use
absolute value symbols when necessary.
If we are told that the variables represent positive real numbers, the absolute value symbol in the answer for the first problem is not needed.
aaaaa 5)5()5())5(()625( 1)4
1(4
4144
14
2)2
1(4)
2
1(2
21422
14 55)5()25( bbbb
7.2 7
Rational Expressions Where the Numerator is greater than 1
644161616 3322 32
3
6422216 62342
342
3
Using Exponent Arithmetic, it’s a little easier
7.2 9
Using Rational Exponents to Simplify Radicals
Simplify
xyyx
yxyxyx
2222
2)2(64
21
21
21
21
21
23
412264 22
7.2 10
Examples
27
8
3
2
3
2
9
432 2
323
22333 9)3(27 32
32
baabba
44
2
6
3
6 16
9
)2(
3
)2(
3
64
2732
32
32
yyyy