English | Español

Try our Free Online Math Solver!

Online Math Solver












Please use this form if you would like
to have this math solver on your website,
free of charge.

Using Powers - Fractional Exponents

Using Powers – Fractional Exponents

Day 1

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

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 x0?

Zero Exponent Rule


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!

• Read pg. 99 - 102
• Pg. 102 #1-10, 39-42
• Pg. 642 Skill 11 evens
• Pg. 642 Skill 12 odds

Day 2

1. (5m-6 )(10n2 )


Fractional Exponents and Radical Form

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


The diameter is about 5.6 cm.

Review – Write an equation to represent each situation. Use k to represent the variation

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

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

Prev Next