Transcript roots and radical exponents tutorial 7a

a
b
c
b
c/a
3/ 4
• x
• 1st - Determine which part of the exponent is the power
and which is the root : remember - POWER/ROOT
– So, in this example”3” is the power & “4” is the root
• 2nd - Now you are ready to write your radical
–
4
x3
8
x5
•
• 1st - Determine which part of the radical is the power and
which is the root
– So, in this example”5” is the power & “8” is the root
• 2nd - Now you are ready to write your rational exponent
– (power/root)
– 5/8
x
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2)
3)
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6)
When multiplying exponents – you add them
When taking exponents to another power - you multiply them
When taking a product to a power - you distribute the exponent to
each variable
When you have a negative exponent - you take its reciprocal
- When the exponent is 0, whatever number is being taken to
the zero power is 1
When you divide exponents - you subtract the exponent in the
numerator with the exponent in the denominator
When you take a fraction to a power - you distribute the exponent
to both the numerator and the denominator the denominator
(numbers correspond w. the previous slide)
xyz 
5 2 4 6
x y z
2/5
4/5
Convert the radical to 3 separate exponents
6/5
(this is the farthest you can go because you cannot multiply
different bases)
y 
2/5 3/4

Distribute exponential fraction to the exponential fraction inside
of the parenthesis
y
6/20

simplify
y
3/10

turn the rational exponent into a radical (power/root)
10
y
3
YOUR DONE :-)
3
2 
3
3 1/ 3
(2 )
(2

3/1 1/ 3
)
2 2
1
Convert the radical to an exponent

Change the exponent in the parenthesis to a exponential
fraction
Multiply the exponential fractions
The product of the exponents is 1, which means the base
remains the same