Caveman Chang EXPLAINS Properties of Exponents aka. Lazy Math

Exponents are another way to say repeated multiplication. The big number is called the base, the number that will be multiplied by itself. The little number on the top right of the base is the exponent, the number of times that the base will be multiplied.

Here are 3 properties of exponents.
1st Property: If you have the same base and you multiply, just add the exponents. (e.g. 2^2 x 2^5 = 2^7)
2nd Property: If you have the same base and you divide, just subtract the exponents. (e.g. 4^7 ÷ 4^3 = 4^4)
3rd Property: If you have the same base and there is an exponent to the power of another exponent, just multiply the exponents. (e.g. (3^3)^2 = 3^6)

Common Errors:
1.) Make sure the base is the same before attempting to add, subtract, or multiply the exponents. If the base is not the same, you cannot combine them in any way. (e.g. 2^2 x 3^5 cannot be combined in any way)
2.) When there are parentheses and exponents, you may not just distribute the exponent. (e.g. (a+b)^2 is not the same as a^2 + b^2)

Practice Problems:
Level 1: Answer is -200
Level 2: Answer is True. If you change the -1 and 1 to negative any number and the same positive number, this statement will still hold true. The first number is negative but if you multiply it an even number of times, it will become a positive number. In this example, -1 multiplied 6 times will become positive 1. The second side of the equation is 1^6 which will stay positive 1 no matter how many times you multiply it. As long the base on the left of the equation is the negative number of the positive number from the right of the equation, this statement will hold true.
(e.g. (-10)^6 = 10^6 , (-25)^6 = 25^6, etc.
Level 3: Answer in base 2 is 2^-1. Using the property, I subtract the exponents so 5 - 6 = -1. Final answer is 1/2 or 0.5

Song: Path Of The Fireflies
By: AERØHEAD
License: Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)

Link to License: https://creativecommons.org/licenses/by-sa/3.0/

Artist Soundcloud: https://soundcloud.com/aerohead

Artist Spotify: https://open.spotify.com/artist/4DH6a3YPKYkhwlNRQKVBxj?si=_D7QUoF9TLOKN0LsqIxERA&dl_branch=1

Artist Youtube: https://www.youtube.com/channel/UCoZbM1a4PKQ6haa2Ap4TSdg