exponents

law 1 : adding

when adding numbers with exponents you add the bases and in this case you will do the same for the exponents. for example:2^4+2^2 would be 4^6

law 2 : subtrcating

when subtracting numbers with exponents you do the same as adding. you subtract the bases and the exponents. base with base and exponent with exponent of course .for example 5^5-2^2 would be 3^3 ( this process is very similar to the process followed when dividing)

law 3: multiplying

when multiplying bases with exponents you would add the bases and themultiply exponents . for example 2^3x4^5 would become 6^15

law 4: dividing

when dividing exponents find and cancel out common factors. for example 3^4/3^2 would be 3^2 or you can just keep your base. then subtract the exponents

heres a video that goes over these 4 laws

Exponent Rules Math Learning Upgrade

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

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

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

radical to rational

when going from radical to rational you do the same steps you just did backwards. so your root becomes your denominator . the bases is still the base and the exponent becomes the nominator. for example ^3√2^4 from this we get 2 ^4/3

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

Converting Rational Exponents and Radicals, Part 1