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Transcript of Rational Exponents & Radicals  teachers.dadeschools.netteachers.dadeschools.net/sdaniel/Rational...
Rational Exponents &
Radicals
Mrs. Daniel Algebra 1
Exponents
Definition: Exponent
• The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.
The Zero Exponent Rule
• Any number (excluding zero) to the zero power is always equal to one.
• Examples:
1000=1
1470=1
550 =1
Negative Power Rule
Let’s Practice…1. 52
2.3
4
−1
3. (3)3
The One Exponent Rule
• Any number (excluding zero) to the first power is always equal to that number.
• Examples:
a1 = a
71 = 7
531 = 53
The Power Rule (Powers to Powers)
When an exponential expression is raised to a power, multiply the exponents.
Try these…
1. (w4)2 2. (q2)8
3. (x3)4
Products to Powers
(ab)n = anbn
Distribute the exponent/power to allvariables and/or coefficients.
For example:
(6y) 2 = (62)(y2)= 36y2
(7x3)2 = (7)2(x3)2 = 49x6
Let’s Practice…1. (5x2)2 4. (6x4)2
2. (3wk3)3 5. (n5)2(4mn2)3
3. (2y)4 6. (5x2)2
The Quotient Rule
Let’s Practice…
Power of a Fraction
Let’s Practice…
3. 3
4
−2
Simplifying Radicals
Radical Vocab
How to Simplify Radicals
1. Make a factor tree of the radicand.
2. Circle all final factor pairs.
3. All circled pairs move outside the radical and become single value.
4. Multiply all values outside radical.
5. Multiply all final factors that were not circled. Place product under radical sign.
Let’s Practice…
1. 225 2. 300
Let’s Practice…
3.1
494. 120
How to Simplify Cubed Radicals
1. Make a factor tree of the radicand.
2. Circle all final factor groups of three.
3. All circled groups of three move outside the radical and become single value.
4. Multiply all values outside radical.
5. Multiply all final factors that were not circled. Place product under radical sign.
Let’s Practice…
1. 3375 2.
364
Simplifying Rational
Exponents
Review: Radical Vocab
Code: Fractional Exponents
Rewrite each of the following as a single power of 7:
1. 7
2. 37
3. 73
4. 349
Let’s Practice #1
Rewrite each of the following in radical form:
1. 51
2
2. 51
3
3. 53
2
4. 5−1
4
Let’s Practice #2
Let’s Practice #3
Simplify, if possible:
1. 81
3
2. 161
2 + 271
3
3. 811
4 + 91
2
4. 45
2  43
2
Let’s Practice #4
Which is equivalent to a1
2 ∙ b3
4?
A. ab3
B. ab3
C.3a2b4
D.4a2b3
Which is equivalent to 3a2?
A. a3
2
B. a2
3
C. a1
6
D. a6
Let’s Practice #5
Let’s Practice #6
Simplify. Rewrite each of the following as a single power of 7.
1. (491
3 )(7−1
4 )
2. 37
7
3. Rewrite 8 ⋅ 22
5 as a single power of 2.
Let’s Practice #7
Rewrite as radical expressions, then simplify, if possible:
1. 12𝑎2
3
2. 6𝑥5
2
3. 64𝑎4
5
Mini Quiz
Is each statement, true or false. Explain!!!!
Applications
Applications
Applications
The volume of a cube is related to the area of a
face by the formula V = 𝐴3
2. What is the volume of a cube whose face has an area of 100 cm2
Rational & Irrational Numbers
Rational Numbers• Any number that can be expressed as the
quotient or fraction 𝑝
𝑞of two integers.
• YES:
– Any integers
– Any decimals that
ends or repeats
– Any fraction
• NO:
– Never ending decimals
Irrational Numbers
• Any number that can not be expressed as a fraction.
• Usually a neverending, nonrepeating decimal.
• Examples:
𝜋
2, 5
1.2658945625692….
Let’s Practice…
Rational or Irrational.
1.2
17
2.1
3
3. 0
Will it be Rational or Irrational?
Sums:
Rational + Rational =
Rational + Irrational =
Irrational + Irrational =
Products:
Rational x Rational =
Rational x Irrational =
Irrational x Irrational =
Rational or Irrational?
1. Is the sum of 3 2 and 4 2 rational or irrational?
2. Is the sum of 4.2 and 2 rational or irrational?
3. Determine if the product of 3 2 and 8 18is rational or irrational.
Advanced Rational
Expressions