I think my teacher is wrong, do you agree with me???

ironsheep said:
Why are the rules the way they are?? What determines them to be true, like if you gave someone two pieces of candy and then gave them another two pieces of candy, then you gave that person 4 pieces of candy( not 5, not 4.5, not 4.1). So when would all these exponents be actually used in real life?? What is the practical day to day approach to this stuff? Also, for step one, why can't you separate them out like I did in my images?? Why are the numbers trapped under the hood sign thing??
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@ronsheep, it seems that either you are a TROLL or just a very basic naive learner. Which are you?
 
It also seems pka that you can't think abstractly and philosophically--- you never once thought why you had to learn this stuff?
 
There are several reasons why to learn this stuff. But the one that is most relevant to most students is that virtually all of physical science and technology (and many of the things that depend heavily on technology) are based on mathematics. You cut yourself off from many of the really promising adult careers if you are incapable of using mathematics. It is like writing: you can flip burgers without knowing how to write, but you cannot get a job as a lawyer if you cannot write comprehensible, persuasive prose.
 
Wow, I got a business degree and we didn't have to learn any of this stuff--- even in my accounting classes, we didn't do anything like that.
 
Here is the logic
By definition xa = x*x*x*...*x, a times. So for example, x6 = x*x*x*x*x*x (note that I multiplied x by itself 6 times.)

Now consider xa*xb. Now we are multiplying what is to the left of the multiplication symbol (or the understand multiplication symbol) by what is to the right of the multiplication symbol. So we are NOT multiplying x and x but rather we are multiplying xa and xb.

Now xa*xb = (x*x*x*...*x) * (x*x*x*...*x) so there are a x's and then b x's for a total of a+b x's

So xa*xb = (x*x*x*...*x) * (x*x*x*...*x) = xa+b

Here is a concrete example. x3*x4 = (x*x*x)*(x*x*x*x) = x*x*x*x*x*x*x = x7

After understanding the above you can just add the exponents right away. ex: x5*x7=x12

Now what about (x3)4. Well this mean x3*x3*x3*x3= (x*x*x)*(x*x*x)*(x*x*x)*(x*x*x) = x*x*x*x*x*x*x*x*x*x*x*x = x12. Now if you look at it carefully you will see that the 12 came from adding 3 to itself 4 times which is simply 3*4. So we multiply the exponents. For example, (x7)5= x35

For now you need to accept these rules work for non-positive integers as well (that is the rule works for fractions, decimal numbers and negative numbers)
 
ironsheep said:
Wow, I got a business degree and we didn't have to learn any of this stuff--- even in my accounting classes, we didn't do anything like that.
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Accounting just uses arithmetic. Math is very different from accounting. You got a business without taking calculus?
 
Jomo said:
Accounting just uses arithmetic. Math is very different from accounting. You got a business without taking calculus?
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Yep, I got a business degree without having to do calculus, that stuff was in high school. How about you?
 
If one takes calculus in high school (and gets college credit) then yes I would consider that they took calculus for their degree (If their degree required it) even though they took it in high school.

Are you saying that you took calculus in high school?

For the record, I do feel that a business student should have to take calculus. Now if your business program did not have this requirement that is nothing against you at all and I apologize if you felt that way.
 
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