Rational Exponents 10. 10. 2 2 1. Evaluate rational exponents. 2. Write radicals as expressions raised to rational exponents. 3. Simplify expressions with rational number exponents using the rules of exponents. 4. Use rational exponents to simplify radical expressions.
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Rational Exponents 10.2 1.Evaluate rational exponents. 2.Write radicals as expressions raised to rational exponents. 3.Simplify expressions with rational.
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Rational Exponents10.210.2
1. Evaluate rational exponents.2. Write radicals as expressions raised to rational
exponents.3. Simplify expressions with rational number exponents
using the rules of exponents.4. Use rational exponents to simplify radical expressions.
2505
25251
5
12
1
Integer ExponentsInteger Exponents
25
32 xx 5x
32x
432ba 128ba
6x
Integer ExponentsInteger Exponents
2/116 2/124
Rational ExponentsRational Exponents
2
12
4
441
2/125 2/125 2
12
5
551
3/18 3/132 31
32
221
16
25
3 8
New notation for a familiar concept!
Denominator is the index (root) of the radical.
3/127 3273
Evaluate:Evaluate:
2/125 525
5/132 2325
3/1343 73433
4/181 3814
Evaluate:Evaluate:
4/181
3/11000 1010003
3/18 283
Not a real number
3/18
21
81
81
33/1
4 81
2/122a a22
Rewrite in Radical Notation:Rewrite in Radical Notation:
8/1w
2/13x 3 x
8 w
2/34 32/14
Rational ExponentsRational Exponents
32 8
Numerator is the power.
2/34 2/134 2/164 8
ba
xpower
root
Generally easier to find the root first and then the power.