none
i prefer angles and COORS
Angles go under Geometry.
From Google:
Coordinate is where algebra meets geometry
i dont like geometry but i like trig
sorry I havent been posting back, I was just confused
It’s ok. This can be pretty complicated stuff. So let’s break it down into smaller pieces.
First, let’s understand exponents.
Summary
We can do that by thinking of how multiplication and addition relate to each other.
3 * 5 is another way of saying add 5 to itself 3 times. That’s why we call them times tables!
3 * 5 = 5 + 5 + 5 → 5 + 5 = 10, then add 10 more 5 → 10 + 5 = 15
When you first started learning multiplication, it might have been a little confusing why you would bother. You could just add like above instead, right? But eventually you started to see how much faster and useful multiplication can be, rather than adding “3” five times.
Ok, here’s where we make a little leap.
Exponents use multiplication much like multiplication uses addition.
53 = 5 * 5 * 5 → 5 * 5 = 25, and then one more * 5 → 25 * 5 = 125
25 = 2 * 2 * 2 * 2 * 2 = 32
“Base” is the big number (in this example, the 5)
“Power” or “Exponent” is the small superscript number (in this case, it’s 3)
The rule is to multiply the base times itself as many times as the exponent.
Important note: Even though 3 * 5 = 5 * 3, it does not work that way for exponents. 53 does NOT equal 35
Special Rules: Any base to the power of 0 (except 0 itself) is equal to 1. Any base to the power of 1 is equal to itself.
345820 = 1
anyOtherNumber0 = 1 (always equals 1)
- special, just for 0, 00 = 0
345821 = 34582
anyNumber1 = anyNumber (always the same as the base)
01 = 0
Ok, your turn:
63 = ?
24 = ?
112 = ?
216
36
22
I did this mental, cuz im lazy, so might be wrong
Try one more time with 112 = ?
(The others were correct)
121
2000000000000000000
(yes discourse this is complete)
Excelente! (that’s Spanish for excellent)
Ok, so now let’s work with exponents a little bit. To multiply exponents of the same base, you add the powers together. To divide, you subtract the powers.
Summary
34 * 33 = 37
34 / 33 = 31
You can even have negative powers. That is like dividing instead of multiplying. So you just put the whole thing into the bottom of a fraction.
2-3 = 1 / 23 = 1/8
You CANNOT put them together if they have different bases.
33 * 23 = ?
You have to resolve them individually:
33 = 27
23 = 8
27 * 8 = 216
Your turn:
26 / 23 = ?
5-3 = ?
53 * 52 = ?
2 power 3 (no idea how to do small numbers)
I dont really get the part with the negatives…
5 power 5
A<sup>B</sup>
is how you type out:
AB
It is the HTML tag for “superscript”. (I had to look it up myself to figure out how to show it.)
It is also acceptable to use the “^” (shift + 6 on the keyboard) like this: A^B
Your answers are correct.
Let’s talk about the negative exponents.
Summary
Imagine you want: 2-2
What this really means is “divide” by 22
Just like how positive exponents mean multiply by this many times, how would you “take away” by this many times? You divide them.
To make something “divided by”, you turn it into a fraction with 1 on top and the rest on the bottom.
Like 6 / 3 is the same as 6 * 1/3
So we can show negative exponents the same way as the " * 1/3"
So 2-2 is “divide by 22”, which is the same as (1 / 22)
2-2 = 1 / 22 = 1/4
Does that make sense? Kinda, ish?
Remember also that when you divide by exponents, you subtract the power and when you multiply, you add them.
You treat those signs the same way as you normally would with addition/subtraction. So dividing by a negative exponent is really just adding the powers.
24 * 2-2 = 22 → (4 + -2)
24 / 2-2 = 26 → (4 - -2) → minus negative 2 is the same as adding 2
2-4 * 22 = 2-2 → (-4 + 2) → also written as 1 / 22
If the whole idea of dividing for negative exponents is hard to understand, you can think of it this way. Let’s say you start with 100. You want to multiply it by itself a negative number of times, that is hard to picture, but you know the answer should be less than 10. If you did it just once, you would have
10-1 = 1 / 101 = 1 / 10
That kinda makes sense, because you are taking away as much as you would be increasing if the exponent were positive. But it isn’t all the way down to zero, it still has some value.
So if you were doing that twice: 10- 2, it’s like 1/10 * 1/10, which is 1/100 or 1/10-2.
Or try thinking about it like this:
45 / 42 = 45 * (1 / 4 2)
You already know you solve (5 - 2 ) to get the answer 43
And you would also subtract (5 - 2) if the problem was written: 45 * 4-2
So logically, 4-2 must be the same as 1 / 42
If you are still confused, look at Negative Exponents
Ok, you try:
Write this as a fraction: 5-3
Solve :
42 * 4-4 = ?
3-3 / 3-5 = ?
54 / 52 = ?
Imma send my answers in PM
ANowaythisworksomgitsworkingthisislikespam,iwillstopnow…
Please do not spam. It’s not about Maths.
okdokayletstalk in normal size lol
4-2
32
52
Sorry for taking so long to respond
Woot! That’s absolutely correct. (Well done especially with: 3-3/ 3-5 = ? That one was extra tricky.)
I’ll put together the next bit very soon. Also, welcome back to “math for keeners”.
it’sworkingig
Qwerty, you’re getting to the point where you’re kind of spamming to use that special font.