Chapter 9 section 1 Rational exponents and radical expressions

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Chapter 9section 1Rational exponents and
radical expressions
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Review Radicals
Square Root
Cube Root
Fourth Root
Fifth Root
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Review
What do you multiply by itself to get 4?
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Review
What do you multiply by itself 3 times to get 27?
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Review
What do you multiply by itself 4 times to get 16?
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Fractions as exponents
as exponent means
as exponent means
as exponent means
as exponent means
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Example 1
Rewrite the expression as a radical expression
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Example 2
Rewrite the expression as a radical expression
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Example 3
Rewrite the expression as a radical expression
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Example 4
Rewrite the expression as a radical expression
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Fractions as exponents
as exponent means
as exponent means
Numerator is 1
as exponent means
as exponent means
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Fractions as exponents
If the numerator is not 1, it becomes the
exponent inside the radical.
In other words, the top number stays an
exponent. The bottom number becomes the root.
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Example 5
Rewrite the expression as a radical expression
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Example 6
Rewrite the expression as a radical expression
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Example 7
Rewrite the expression as a radical expression
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Example 8
Rewrite the expression as a radical expression
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Example 9
Rewrite the expression as a radical expression
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Example 10
Rewrite the expression as a radical expression
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Example 11
Rewrite the expression as a radical expression
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Review
When you have a power raised to another power,
you multiply the exponents.
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Review
When you multiply a whole number and a fraction,
just multiply the top and leave the denominator
the same.
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Review
When you multiply a whole number and a fraction,
just multiply the top and leave the denominator
the same.
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Example 12
Rewrite the expression as a radical expression
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Example 12
Rewrite the expression as a radical expression
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Example 13
Rewrite the expression as a radical expression
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REVERSE
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Example 14
Rewrite the radical expression as an exponential
expression
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Example 15
Rewrite the radical expression as an exponential
expression
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Example 16
Rewrite the radical expression as an exponential
expression
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Example 17
Rewrite the radical expression as an exponential
expression
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Example 18
Rewrite the radical expression as an exponential
expression
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Example 19
Rewrite the radical expression as an exponential
expression
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Example 20
Rewrite the radical expression as an exponential
expression
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Simplifying radical expressions
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Square Roots
Here are the 1st 15 perfect square roots
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Cube Roots
Here are the 1st 5 perfect cube roots
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fourth Roots
Here are the 1st 5 perfect fourth roots
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fifth Roots
Here are the 1st 3 perfect fifth roots
All of these roots are listed in chart on p 522
of your textbook
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We use the chart to simplify roots with numbers.
Now, lets talk about how we simplify square
roots, cube roots, fourth roots, and fifth roots
with variables.
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Square Roots
To take square root of variable expressions,
divide the exponents by 2.
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Example 21
To take square root of variable expressions,
divide the exponents by 2.
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Example 22
To take square root of variable expressions,
divide the exponents by 2.
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Example 23
To take square root of variable expressions,
divide the exponents by 2.
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Example 24
To take square root of variable expressions,
divide the exponents by 2.
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Example 25
To take square root of variable expressions,
divide the exponents by 2.
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cube Roots
To take cube root of variable expressions, divide
the exponents by 3.
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Example 26
To take cube root of variable expressions, divide
the exponents by 3.
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Example 27
To take cube root of variable expressions, divide
the exponents by 3.
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Example 28
To take cube root of variable expressions, divide
the exponents by 3.
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Fourth Roots
To take fourth root of variable expressions,
divide the exponents by 4.
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Example 29
To take fourth root of variable expressions,
divide the exponents by 4.
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fifth Roots
To take fifth root of variable expressions,
divide the exponents by 5.
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Example 30
To take fifth root of variable expressions,
divide the exponents by 5.
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Simplifying radicals
Lets look at some examples with coefficients and
variables.
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Example 31
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Example 32
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