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Exponents: Rational exponents
- Lesson: 17:45
- Lesson: 27:45
- Lesson: 2a2:00
- Lesson: 2b4:56
- Lesson: 3a0:49
- Lesson: 3b0:57
- Lesson: 3c2:11
- Lesson: 3d4:25
- Lesson: 3e13:57
- Lesson: 4a0:49
- Lesson: 4b0:57
- Lesson: 4c2:11
- Lesson: 5a0:27
- Lesson: 5b1:25
- Lesson: 5c1:39
- Lesson: 5d2:03
- Lesson: 5e2:46
Exponents: Rational exponents
Basic Concepts: Convert between radicals and rational exponents
Related Concepts: Power rule
Lessons
• nx=xn1
• x−n1=xn11=nx1
• xnm=nxm
• x−n1=xn11=nx1
• xnm=nxm
- 1.prove: a83=8a3
- 2.Simplifying Expressions Using: nx=xn1
Simplify the following expressions if possible.a)6431
1641b)(−16)41
(−32)51 - 3.evaluate:a)(25)21b)(−4)21c)(10)83d)(8)35e)(−32243)−52
- 4.Simplifying Expressions Using: x−n1=xn11=nx1
Simplify the following expressions.a)27−31b)6x1c)(64x8)−21 - 5.Simplifying Expressions Using: xnm=nxm
Simplify the following expressions if possible.a)2x6b)2523c)(−125)−32d)36x16y24e)3−216a9b24c117
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20.
Indices
20.1
Indices: Product rule (ax)(ay)=a(x+y)
20.2
Indices: Division rule ayax=a(x−y)
20.3
Indices: Power rule (ax)y=a(x⋅y)
20.4
Indices: Negative exponents
20.5
Indices: Zero exponent: a0=1
20.6
Indices: Rational exponents
20.7
Combining laws of indices
20.8
Scientific notation
20.9
Convert between radicals and rational exponents
20.10
Solving for indices
Don't just watch, practice makes perfect
Practice topics for Indices
20.1
Indices: Product rule (ax)(ay)=a(x+y)
20.2
Indices: Division rule ayax=a(x−y)
20.3
Indices: Power rule (ax)y=a(x⋅y)
20.4
Indices: Negative exponents
20.6
Indices: Rational exponents
20.7
Combining laws of indices
20.8
Scientific notation
20.9
Convert between radicals and rational exponents
20.10
Solving for indices