I know this isn't really a specific question. Could someone please explain negative exponents to me, and how to solve them? I am in cyber school and I just don't understand. Thanks in advance.

Question

anonymous · Answer

While not intuitively easy to understand, they make a lot of sense when you think about them using the so called rules of exponents.

anonymous · Answer

Are you familiar with these?

anonymous · Answer

Yes, the lessons I'm on are full of examples but they are just a blur to me. They don't explain the steps they are taking to get the answer. Could you give me an example and tell me what you are doing?

anonymous · Answer

Here they are: www.rock.uwc.edu/academics/tutoring/lsc/handouts/Properties%20of%20Exponents.pdf

anonymous · Answer

I like to use numbers on these rules as they make everything a lot easier to visualize.

anonymous · Answer

So you are be familiar with positive exponents right?

anonymous · Answer

yep :) , and that make it a lot easier to understand. I think I get it :)

anonymous · Answer

*makes

anonymous · Answer

For instance, 2^3 is equal to 2*2*2. x^3 is equal to x*x*x. and x^m would be just be x multiplied by itself m times.

anonymous · Answer

so like 5^3 would be 125?

anonymous · Answer

Where am I heading with this? Well, you can use the definition of an exponent (x multiplied by itself m times) to obtain the other properties.

anonymous · Answer

ok :) thanks that pdf really helped clear things up for me :)

anonymous · Answer

The power rule should be the easiest to see as you are raising a number that is already being raised by another. So with our example of 5^3=5*5*5, we can say that (5^3)^2 would be equal to 5*5*5 (just like we had earilier established through the defintion of an exponent) times itself. The question here is what is itself? Well In the case of 5^3, 5 was itself, in the case of (5^3)^2, 5^3 is itself, 2 is the number of times. So we would end up with something (5^3)*(5^3), (itself multiplied two times), or (5*5*5)*(5*5*5).

anonymous · Answer

oh! ok! I get it :) Thank You SOOOOOOO much :) I'm becoming a fan :)

anonymous · Answer

What can you deduct from this, well if 5^3 is 5*5*5, where you have 5 multiplied by itself three times, then 5*5*5*5*5*5 is equal to 5^6 (remember that multiplication is associative, that is you can group multiplication any way you want to like 5*(5*5)=(5*5)*5.

anonymous · Answer

So very briefly the power rule states that (x^m)^n is equal to x^(m*n) like in the case of (5^3)^2.