What is an exponent? An exponent is a power that is represented by a number beside the base number. Exponents usually contain two numbers, one called the base and one number called the number of copies exponent. The base number is the number that gets multiply by the exponent. The example you have 
which would be 2x2x2, each time the number gets bigger and each time you multiply your answer by two. So, it would have been 2×2=4, 4×2=8 would be equivalent to (8). When you add negatives to the equations it will affect the outcome. If your number is negative in no parentheses you will have a negative outcome because exponents are LAZY! An example is 
which is going to be -2x2x2 which is -8, however, if that was in parentheses then it would have been (-2)x(-2)x(-2) which is positive 8. Why? Because exponents are lazy it means that they would like the easy way out of things. The example you have the exponent which is the 3, in this equation is just looking at the number in front of it which is 2 our base number. It knows that there’s something else there it just chooses to act like there’s nothing there. That’s why our outcome is negative! It looks and knows there’s a negative sign, it only puts that for the first base when putting into exponential form. Then it is just our simple rule of negative and positive adding/subtracting/multiplying/dividing, negative + negative = positive, positive + positive = positive and the rest of the possible equations are with a negative outcome (unless a thug a war question). This rule is also applicated when you are subtracting! However, it is more complicated than adding, let’s say you have 
, just to clarify it is different than just because in this case, the exponent has no choice, but to take the whole equation because it is in parentheses. According to the rule of negative + negative = positive, the answer would be a positive {(-2)x(-2)x(-2)= 8). Anyway, when subtracting you have to remember that there’s a negative sign to start with! Assuming you have a positive number to start with and it’s the number after the subtracting sign is it possible that, that number turns into a negative?! Or when you have a negative number instead of the positive and your subtracting could it just be a positive sign that feels apart, because it isn’t having the best day?-Ms. Burton.
What is the difference between evaluating and simplifying? When a question is asking you to evaluate something that simply means solve the equation. The example, 
x 
, just do the equations 5+2=7 your answer is 
. Simplifying means simplify your exponent leaving it in exponent form rather than actually solving the exponent (equations). The example, $latex 8^4$ is the same thing as 
. That would be the difference.
Multiplication/Division law and why it works! What is the multiplication law of an exponent? It’s obviously tied into multiplying! Well at one point, yes but sometimes not at all, it’s more or less adding than multiplying. What? Think of it like this you have 
x 
, *note that they have the same base, then if they do have the same base add the two EXPONENTS together. Do not add the bases together, just the exponent. The example x 
takes the exponents, which is the 6 and 2 and add the two together. That creates 8, so your answer is The multiplication law is, when multiplying two different exponents with the same base, you just add the two exponents together and leave it with the same base. The same thing applies to negatives! For example, you have 
x 
6 – 5= 1, it will stay positive unless the 5 was bigger than the 6. Division law is very similar to multiplication law, they are practically opposites! The division law says that, if you are dividing with the base then you may just subtract the two exponents. Assuming only if you have the SAME base! The example, 
– $latex4^5$, which is just 3-5= -2 so your answer is negative. You don’t need to have a negative sign in the equation, to have a negative outcome! An example using negatives 
– 
= 
. Why? Because, -3 – 9= 6!
Power of a power law and why it works! Power law! What is a power law? A power law is when you have an exponent with another exponent on the outside like this one 
, which just means that you are multiplying 6×3, which will then equal to 18. It can be applied to negatives as well. Let’s say your equation is 
which means that it will be 5 x -9 which is equal to -45, being that our simple rule of negatives and positives. So, if we had to give an explanation to the power law I would say, the power law is when two exponents get multiplied together!
One more thing you learned about exponents! Power law of 0! What is the power law of 0? The power law of 0 is very simple! It is just to say that is you have an exponent of 0 anywhere your automatic answer for that exponent is 1! The example, 
would mean no solving needed to do your answer is just simply 1!
Power law of 1! What is the power law of 1? The power law of 1 is less simple than 0, but still pretty easy, in my opinion. Anything in that has the power of 1 is the same as it was it will not change! Your base stays the same and you dont need to do any work. For example, 
= 6! Easy right.