Caveman Chang EXPLAINS Properties of Exponents PART 2

Here are 3 properties of exponents.
1st Property: Any number to the exponent 0 equals 0. The only exception is if the base is 0 then 0^0 is undefined.
(e.g. 1000^0 = 1)
2nd Property: Some number to the negative exponent is the same as 1 over that same base but to the positive exponent. The only exception is if the base is 0 because we can never divide by 0. (e.g. 7^-4 = 1/(7^4))
3rd Property: If you want to distribute the exponent, make sure the function inside the parentheses is either all multiplication or all division. You cannot do this if there is addition or subtraction in the parentheses.

Common mistakes:
1.) The zero exponent does not make that equal 0. Any number as the base to exponent 0 will equal to 1. Unless the base is 0, then the answer will be undefined.
2.) A negative exponent does not make the answer negative. It tells us how to orient the problem but does not tell if the solution is positive or negative.
3.) Distributing the exponent to the parentheses when it is addition or subtraction. Distributing exponents can only apply to muliplication or division.

Practice Problems:
Level 1: Answer is 1
Level 2: Answer is 4
Level 3: Answer is True. On the left side of the equation, the outside exponent 3 is multipled by -4, making it -12. On the right side of the equation, the inside exponent -3 is multiplied by 2, then multipled by 2 again, making it -12. If i replace the 7 by any number, it will still hold true.

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