Download Presentation
7.1/7.2 Nth Roots and Rational Exponents

Loading in 2 Seconds...

1 / 12

# 7.1/7.2 Nth Roots and Rational Exponents - PowerPoint PPT Presentation

7.1/7.2 Nth Roots and Rational Exponents. How do you change a power to rational form and vice versa? How do you evaluate radicals and powers with rational exponents? How do you solve equations involving radicals and powers with rational exponents?. The Nth root. Radical. Index Number.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about '7.1/7.2 Nth Roots and Rational Exponents' - sadie

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 7.1/7.2 Nth Roots and Rational Exponents

How do you change a power to rational form and vice versa?

How do you evaluate radicals and powers with rational exponents?

How do you solve equations involving radicals and powers with rational exponents?

The Nth root

Radical

Index Number

n > 1

The index number becomes the denominator of the exponent.

Radicand

Radicals
• If n is odd – one real root.
• If n is even and
• a > 0 Two real roots
• a = 0 One real root
• a < 0 No real roots
Example: Radical form to Exponential Form

Change to exponential form.

or

or

Example: Exponential to Radical Form

Change to radical form.

The denominator of the exponent becomes the index number of the radical.

Example: Evaluate Without a Calculator

Evaluate without a calculator.

Example: Solving an equation

Solve the equation:

Note: index number is even, therefore, two answers.

Rules
• Rational exponents and radicals follow the properties of exponents.
• Also, Product property for radicals
• Quotient property for radicals
Adding and Subtracting Radicals

Two radicals are like radicals, if they have the same index number and radicand

Example

Addition and subtraction is done with like radicals.

Example: Addition with like radicals

Simplify.

Note: same index number and same radicand.

Add the coefficients.

Example: Subtraction

Simplify.

Note: The radicands are not the same. Check to see if we can change one or both to the same radicand.

Note: The radicands are the same. Subtract coefficients.