Evaluating rational expressions

Evaluating rational expressions

Standard Algebra II

Rewriting rational expresions

• The bottom of the fraction, becomes the root index.

• The top number becomes the power.

Multiple Choice

In   $27^{\frac{1}{3}}$  Which number will be the root index?  

• 1

• 3

Multiple Choice

Given $16^{\frac{1}{4}}$ what number will be the root index

• 1

• 4

Multiple Choice

Given $4^{\frac{3}{2}}$  What is the root index?

• 2

• 3

Multiple Choice

What is $625^{\frac{3}{4}}$ written as a radical?

Multiple Choice

What is $\left(-32\right)^{\frac{2}{5}}$ written as a radical? 

Solving a rational expression

• After we set it up as a radical...

• We solve the radical!

• First solve the radical

• Then do the exponent

Oh! about the negatives....

When you have a negative exponent you move it to the bottom of the fraction... (If there is no fraction you put it under 1.)

Multiple Choice

How would you rewrite $81^{-\frac{3}{4}}$ as a radical? 

Multiple Choice

OK, now solve $81^{-\frac{3}{4}}$  

•  $\frac{1}{3}$  

•  $\frac{1}{12}$  

•  $-3$  

•  $\frac{1}{27}$  

Oh, about the other negative!

If you have a negative inside an odd root. You can pull out a negative. If it's an even root you pull out an i.