# Properties of Rational Expressiones

### Austin Acuff

## Rational Exponets and Radical Notation

## explenation

Instead of finding the root of 5 you can move the 3 over to the other side take away the root and put 1/3 to the right as a power. You would get the 1 because the 5 is to the power of 1. So you would get 5 to the 1/3 power.

## Product of Powers Property

## explenation

To start the problem you would not multiply 12 X 12 instead you would add the powers ½ + 3/2 and you would get a 2 power and the last thing to do is multiply 12X12 an get 144. They have to have the same base to be a product of powers property which in this case would be 12.

## Quotient of Power Property

## explenation

The base problem is a^b/a^c = a^b-c. So you would void dividing 125 by 125 and instead subtract the powers 2/3 minus 1/3. Once you get the answer you would type into the calculator 125 ^1/3 and you would get 5 as your answer.

## Power of a Power Property

## explenation

You would start by writing the problem out. (8^2/3) (8^2/3) (8^2/3)=8^2/3 +2/3 +2/3 = 8^2. Once you get to that part you would simply times 8 X 8 and get your answer as 64.

## Power of a Product Property

## explenation

You would foil out the problem first and get 16^1/2 X 25^1/2. You would cut each number to its root and for 16 you would get 4 and for 25 you would get 5. Then you simply multiply the problem and get 20

## Power of a Quotient Property

## explenation

You would start by foiling out the ¼ problem. Then you would find the root of each number and you will find your answer.