# Using Powers - Fractional Exponents

# 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: 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}?

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} )(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 #12-29, 32, 34, 36

• Practice 14 #9-26

Prev | Next |