Question

Can someone explain all of the properties of exponents slowly and piece by piece for me?

Answer 1

What do u mean by slowly?

Answer 2

Like step by step

Answer 3

What properties do you want to know about?

Answer 4

All of them):

Answer 5

Do you have a math book?

Answer 6

Yeah, but I'm not really good at understanding textbook style of writing. I need to hear it in words I would use,

Answer 7

Well then write down the formula you don't understand and I'll explain what it means.

Answer 8

Definition of Integer Exponents:
Let a be a real number. (what's a real number?)
If n is a natural number (what's that?), then a^n = a x a x a.... how many n times.
If a is nonzero (whaaatt), a^0 = 1 (what......)
If n is a natural number, then a^-n = 1/a^n (how did they get that?)

Answer 9

1) A real number is any number you can think of that does not have to do with the complex numbering system. So like 3 or -5 or 5.3 or -15.4 or 8.5 ect...
2) A natural number is any single digit number like 1 or 2 or 3 or 4 or 13. A number that does not have a decimal part to it.
3) So if 'a' is a real number lets say 5.3 and you do a^0 you will get 1 so 5.3^0 = 1
4) Okay so when a number lets say 9 is taken to a negative exponent lets say -2, written like this 9^(-2) Then it would be the same as writing 1/(9^2)

Answer 10

Does that make more sense?

Answer 11

I don't understand the third and fourth one :/

Answer 12

Alrighty, well for the third one if any number is taken to the "zero power" so x^0 then the answer will always be 1. No matter what. even if x is 9561
For the fourth one you have to understand about reciprocals like 2 and 1/2. And a negative exponent just makes that number it's reciprocal number. (just flip flopping the numerator and denominator and the denominator is always 1 if it is not written.)

Make more since? or was that confusing?

Answer 13

Yeah it does now, but WHY is it that x^0 is 1. Shouldn't it be zero because it's 0 times?

Answer 14

Well what you are actually doing when you exponentiate a number (lets say 3) is you are multiplying 3 by its self multiple times. If you wanted to go to the fifth power you would be doing 3^5 = 3*3*3*3*3 however 3^5 also equals 1*3*3*3*3*3 (because 1 can be multiplied by any number and that number will not change).
So if you have multiplying by the zeroth power you would have no 3's and you would be left with a 1.

Answer 15

Ohhhhh okay. Thanks :)

Answer 16

Your welcome :D