I’m doing my GED and passed that math part but this never came up. I saw it on a meme and am lost.
Help!!??
In: 9770
If we want to go from 2^2 to 2^3 we simply multiply by 2.
2^2 = 4 -> 4×2 = 8 = 2^3
But now let’s try going backwards. If we want to go from 2^3 to 2^2, since we multiplied going forwards we will divide going backwards.
2^3 = 8 -> 8/2 = 4 = 2^2
Now let’s keep applying that logic:
2^3 = 8
2^2 = 4 (8/2)
2^1 = 2 (4/2)
2^0 =1 (2/2)
And we can keep going:
2^-1= 0.5 (1/2)
2^-2 = 0.25 (0.5/2)
And so on.
Works with every number, try it out!
Edit: this is probably too late of an edit but since a lot of people are mentioning 0. I just want to say this is not an explanation of how exponents work, but rather a proof to show why x^0 = 1, given x is an integer and not 0.
If you want an explanation of how exponents work, since all our teachers did a terrible job, check out this [article](https://betterexplained.com/articles/understanding-exponents-why-does-00-1/) I found. I thought it did a great job at explaining the how.
Also please guys I don’t care for internet points, instead of giving me an award buy yourself a chocolate bar (idk how much awards cost? Does it cost the same as a chocolate bar? 😅)
Here’s the explanation I like best:
2¹=2. Happy enough? Now multiply it by 2.
2¹×2=2²=4. And again.
2²×2=2³=4×2=8. And again.
2³×2=2⁴=8×2=16. And so on.
So multiplying by 2 is the same as increasing the power of 2 by 1. Now, dividing is just like undoing division. So dividing just *decreases* the power by 1, i.e.
2⁴÷2=2³=16÷2=8.
2³÷2=2²=8÷2=4.
2²÷2=2¹=4÷2=2.
So…
2¹÷2=2⁰=2÷2=1.
And we can push it further and say that negative powers give us fractions (except I can’t write negative powers on here)…
2⁰÷2=2^(-1)=1÷2=½
Former math teacher here – there are very good answers in this thread but in truth they’re explaining it to you like you’re a college undergrad, not like you’re five lmao. So I will try to give a very very simple, fundamental explanation.
Basically – think about what exponents *are*. 2^4 is just 2x2x2x2. So think about how you make 2^4 into 2^3. You divide it, right? Just like you multiply the base number by itself to get a higher exponent, you perform the reverse operation to make a lower exponent.
So 2^1 is 2, that’s self-evident. You turn 2^1 into 2^0 in the exact same way you turn 2^4 into 2^3 – by dividing by 2. What’s 2/2? 1.
This is also why 2^-1 is 1/2, 2^-2 is 1/4, and so on.
I love all these algebraic answers on ELI5.
Everything raised to the power of 0 = 1.
Also: dude, good job coming on here and asking. Good on you getting a GED. My wife was kept out of HS by her family, got a GED and is now an RN.
I find it’s useful to interpret the exponent as “how many times you multiply 1 by the number. So 2^1 is 1 multiplied by 2 one time, i.e. 1 * 2. 2^0 is then 1 multiplied by 2 0 times, i.e. 1.
It also works with negative exponents, if we consider that dividing by a a given number one time is like multiplying by the same number minus-one time.
2^x means “multiply 1 by 2, x times”.
When x is 0, you are multiplying 1 by 2 zero times, or not at all, leaving the original: 1.
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i just always remembered anything to the power of 0 is 1, i have not bothered remembering the reason
My math teacher taught me to think of it like this:
What is a number divided by itself? It equals 1. So 2/2=1, 19/19=1, and so on.
What is 3^7 ÷ 3^3 ? It’s 3^(7-3) = 3^4
So now imagine 3^0 as 3^1 ÷ 3^1 = 3^(1-1) . A number divided by itself is always 1, so 3^0 is also = 1.
Exponent rules dictate that ( 2^x ) / (2^y) = 2 ^(x-y)
For example: 2^3 = 8, 2^4 = 16
Therefore, 2^4 / 2^3 = 2^(4-3) = 2^1 = 2
Or you can express that as (2^4) / (2^3) = (16) / (8) = 2
Now that we’re comfortable with that …
2 / 2 = 1 which is the same as 2^1 / 2^1 = 2^(1-1) = 2^0 = 1
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