# exponents

### By:Kathy Mercado

## the 4 basic laws of exponents

## heres a video that goes over these 4 laws

Exponent Rules Math Learning Upgrade

## roots

## simplifying squar roots

when simplifying square roots you can make a factor tree. within the factor tree you want to find groups of 2 that are the same #. and if you have more than 1 group of 2 you take 1 number from each group and multiply them to get the base which will be on the outside of the root. making your last remaining number in the factor tree your base on the inside or taking the last 2 ungrouped numbers and multiplying them to get the inside of your base. for example in the picture on the right there are 3 groups of containing 2 numbers (in this case being the number 3) since there are 3 groups we will do 3x3x3 giving us 4 as the outside base number. now using the last unused number being 9 giving us 9√9

## heres a video to help

Factoring Numbers with a Factor Tree - kids algebra lesson

## cubed roots

## simplifying cubed roots

when simplifying cubed roots you follow the same exact rules as if you were simplifying a square root. only this time you will be looking for groups containing 3 number instead of 2.for example. in the picture on the left there are 4 groups of 3 made from 2's. since there are 4 groups then we will multiply 2 by itself 4 times (2x2x2x2) this will give us 18(being out outside base) then getting the left over number to be our inside base (4) giving us 4√2

## rational and radical

## putting a rational exponent in radical form

when starting with a rational exponent you want to put into radical form you will take your denominator and make it the root. now you will take your base and put it inside the root, making the nominator the exponent for the base on the inside. for example 2 ^4/3 would become ^3√2^4

## heres another video to help you

Simplifying Radicals - Best Explanation

## going from a radical expression to a rational exponent

## quick video help (skip to 3.15 and end at 3.30)

Converting Rational Exponents and Radicals, Part 1