Rational Exponents

Slates!

1. Factor .

2. Solve.

Solving Literal Equations

Definition: equations that contain several variables
are called literal equations.

Example 1: The fol lowing formula is used by
electricians to determine the total resistance R_total of
two parallel resistors R₁ and R₂. Solve for R₁.

Variation Applications

Three types of Variation

1. Direct Variation

y varies directly as x
y is directly proportional to x

3. Joint Variation y varies jointly as x and z

Steps for solving Variation Problems

1) Write your equation with the given variables
*You have to determine what type of variation you have!
2) Solve for your constant of variation (k)
3) Write your equation again with the
constant you solved for in step 2.
4) Make your prediction.

Three types of Variation

Example 1:
The time T required to empty a tank varies
inversely as the rate r of pumping. If a Briggs
pump can empty a tank in 45 minutes at a rate of
600 kL/min, how long will it take to the pump to
empty the tank at 1000 kL/min?

Roots

Definition: The inverse of raising to a power is called
taking the root.

Parts of a Root

Simplifying Radicals

Example 1: Simplify.

Example 2: Simplify.

Example 3: Simplify.

Example 4: Simplify.

Example 5: Simplify.

Example 6: Simplify.

Example 7: Simplify.

Example 8: Simplify.

SLATES!
Find the Square Root .

SLATES!
Simplify.

SLATES!
Find the Square Root.

SLATES!
Simplify.

Radical Functions and Domain

Example: Evaluate.

Example: Evaluate.

PRACTICE!
Evaluate.

Example 1: Determine the domain.

Example 2: Determine the domain.

Practice: Determine the domain.

Rules of Exponents

Multiplying

Dividing

Rules of Exponents: Review

Raising a power to a power

Raising a product to a power

Raising a quotient to a power

Zero Exponent

Negative Exponent

Building Blocks...

Rational Exponents

New Exp onent Rule !!!

Example 1: Rewrite using exponential notation .

Example 2: Rewrite using radical notation.

Example 3: Rewrite using radical notation.

SLATES!
Rewrite using exponential notation.

SLATES!
Rewrite using radical notation.

Simplifying Expressions with Rational Exponents

Example 1: Simplify

Example 2: Simplify.

Example 4: Simplify.

SLATES!
Simplify.

Example 5: Simplify

Next Class

Example 6: Simplify.

Example 7: Simplify.

Practice. Simplify

That's it for today!

Homework Help Resources:
• The Math Center
• Interact Math
• Algebraic : Radicals

If Time:
Study for
Exam2!

Homework:
• Practice problems from this lesson
MathXL #17
• Reflect on what you have learned
• Prepare for next class' lesson