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Using Powers  Fractional Exponents
Using Powers – Fractional Exponents
Day 1
Warmup
Solve
1. Find the surface area and volume of a sphere with radius r = 4cm.
2. Evaluate and round to the nearest tenth: x^{5} when x = 1.3.
Negative Exponents
Complete the table
Negative Exponent  Decimal  Fraction 
2^{1}  1/2  
2^{2}  1/4  
2^{3}  1/8  
2^{4}  1/16  
2^{5}  1/32 
Using the information from the table, draw a conclusion about negative exponents.
Negative Exponent Rule
Example 1 – Simplify and write answers with positive
exponents.
Zero Exponent
Complete the table
What can we say about x^{0}?
Zero Exponent Rule
Example
Example 2 – Simplify and write answers with positive exponents .
When the exponent is positive, leave it alone!
When the exponent is negative, move it and make it positive!
Homework
• Read pg. 99  102
• Pg. 102 #110, 3942
• Pg. 642 Skill 11 evens
• Pg. 642 Skill 12 odds
Day 2
Warmup
Simplify
1. (5m^{6} )(10n^{2} )
2.
Fractional Exponents and Radical Form
Find
Therefore,,when x 0 and .
Example 1  Rewrite in radical form
Example 2 – Rewrite in exponential form
Example 3 – Find the value of each expression when x = 8 and y = 9.
Example 4 – Suppose a roller coaster car can travel at a
speed of 30 ft/s. What would be
the greatest radius of a vertical loop of a track it could make?
The radius of the track would be about 28 ft.
Example 5 – The diameter of a cylinder with volume V and
height h is given by the
expression
.
Find the diameter, to the nearest tenth, of a cylinder
with volume 200 cm^{3} and height 8
cm.
The diameter is about 5.6 cm.
Review – Write an equation to represent each situation.
Use k to represent the variation
constant.
a. The amount of clay needed to make a square pyramid with
height 1 ft. varies
directly with the square of the length of a base edge.
Solution
V = ke^{2}, where V = amount of clay and e = the base edge.
b. The time it takes to fill a spherical balloon is
directly proportional to the cube
of the radius of the balloon.
Solution
t = kr^{3}, where t = time and r = the radius of the balloon.
Homework
• Read pg. 99  102
• Pg. 102 #1229, 32, 34, 36
• Practice 14 #926
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