Using Powers – Fractional Exponents

Day 1

Warm-up
Solve
1. Find the surface area and volume of a sphere with radius r = 4cm.

2. Evaluate and round to the nearest tenth: x⁵ when x = 1.3.

Negative Exponents
Complete the table

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 x⁰?

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 #1-10, 39-42
• Pg. 642 Skill 11 evens
• Pg. 642 Skill 12 odds

Day 2

Warm-up
Simplify
1. (5m^-6 )(10n² )

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 cm³ and height 8
cm.

Solution

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 = ke², 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 = kr³, where t = time and r = the radius of the balloon.

Homework
• Read pg. 99 - 102
• Pg. 102 #12-29, 32, 34, 36
• Practice 14 #9-26