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Have you ever wondered why: 2⁰ = 1

Here is a simpler answer a layman can understand, by showing it as a pattern.

2⁴ = 16
2³ = 8
2² = 4
2¹ = 2

Notice the pattern that as it goes down one raise to the power of the number or (go down one exponent) that you're dividing by 2 like this:

2⁴ = 16
2³ is: 16 divide by 2 = 8
2² is: 8 divide by 2 = 4
2¹ is: 4 divide by 2 = 2
2⁰ is: 2 divide by 2 = 1
Now you have 2⁰ = 1

So from the pattern above when we get to 2⁰ it becomes 2 divide by 2 = 1.

If math is taught this way from the start, it becomes much easier to use formulas later, because students will understand what the formulas are actually doing instead of just memorising formulas

I can prove it for you

Zico5:
I can prove it for you

Go ahead and invoke the exponential powers!

MindHacker9009:
Have you ever wondered why: 2⁰ = 1

there is a course in mathematics called 'Real Mathematics'.
In this case, you prove by contradiction. If your contradictory proof is wrong then the converse will be true.

Nairaland is not for mathematics... So, let me not bore you with the proof cos it will take like 10 lines.

If you still want the proof... Let me know.

dawnomike:
there is a course in mathematics called 'Real Mathematics'.
In this case, you prove by contradiction. If your contradictory proof is wrong then the converse will be true.

Nairaland is not for mathematics... So, let me not bore you with the proof cos it will take like 10 lines.

If you still want the proof... Let me know.

Na to use scope when u no no something
Oga get out or

Because 2¹ = 2

MindHacker9009:
Have you ever wondered why: 2⁰ = 1

Na all these things wein oyinbo take confuse us. When we cram and memorise all these theories, come pour am out for various exams, we go think say we get sense. Oyinbo go pat us for back, give us Prof. We go dey proud, dey boast say we get highest number of this or that blah blah blah. Ordinary electricity problem we no fit solve.

The answer lies in the meaning of 2 raised to power of n(dont how to come up with superscript on my android keyboard). 2 to power of n means two multiplied by itself n times. 2 to power of zero is therefore 2 multiplied by itself 0 times, and thats 1.

Indices

2⁰ = 2ⁿ⁻ ⁿ
= 2ⁿ/2ⁿ = 1

Indices

2⁰ = 2ⁿ⁻ ⁿ
= 2ⁿ / 2ⁿ = 1

eastOFwest:
Na all these things wein oyinbo take confuse us. When we cram and memorise all these theories, come pour am out for various exams, we go think say we get sense. Oyinbo go pat us for back, give us Prof. We go dey proud, dey boast say we get highest number of this or that blah blah blah. Ordinary electricity problem we no fit solve.

You are right, as none of the answers so far have explained in simple terms why 2⁰ = 1.
They are all just pouring out exponential grammar.

Lets prove by contradiction.

By division.

1. (x^n) /(x^n) = x^(n-n)

2. (2^2) /(2^2) = 2^(2-2)

3. (2^2) /(2^2) = (2×2)/(2×2) = 4/4 = 1.

Also

2^(2-2) = 2^(0)

If 2^(2-2) is equal to (2^2) /(2^2) in equation 2 and since (2^2) /(2^2)is equal to 1 in equation 3. Then 2^(0) = 1.

By multiplication

1. (x^a) × (x^b) = x^(a+b)

2. (2^2) × (2^0) = 2^(2+0)

3. 2^(2+0)= 2^(2) = 4.

Replace 2^(2+0) = 4 (as derived from 3) and insert into equation 2.

So that (2^2) × (2^0) = 4.

(2^2) = 4.

So we have 4 × (2^0) = 4
4(2^0)=4

Divide both side by 4 and make (2^0) the subject of the formula.

(2^0) = 4/4
=1.

If you insert any other non Zero number into the equation, you'll always get 1.

The answers so far are the reason many people run away from math, thinking it's hard when in fact, it's very easy if explained in layman's terms, that even a primary six year old can understand

MindHacker9009:
The answers so far are the reason many people run away from math, thinking it's hard when in fact, it's very easy if explained in layman's terms

There is a very bogus calculation behind it but there is another very simple one

There is a mathematical principle known as the the division property of 1 or exponent rule.

Any item divided by itself equals 1 except zero.

A^3/A^3 = A^(3-3) =A^(0).

Since A^3/A^3 = 1 (division property of 1)
Therefore A^0 = 1.



Q.E.D

Here is a simpler answer a layman can understand, by showing it as a pattern.

2⁴ = 16
2³ = 8
2² = 4
2¹ = 2

Notice the pattern that as it goes down one raise to the power of the number or (go down one exponent) that you're dividing by 2 like this:

2⁴ = 16
2³ is: 16 divide by 2 = 8
2² is: 8 divide by 2 = 4
2¹ is: 4 divide by 2 = 2
2⁰ is: 2 divide by 2 = 1
Now you have 2⁰ = 1

So from the pattern above when we get to 2⁰ it becomes 2 divide by 2 = 1.

If math is taught this way from the start, it becomes much easier to use formulas later, because students will understand what the formulas are actually doing instead of just memorising formulas

Updated:

Here is a simpler answer a layman can understand, by showing it as a pattern.

2⁴ = 16
2³ = 8
2² = 4
2¹ = 2

Notice the pattern that as it goes down one raise to the power of the number or (go down one exponent) that you're dividing by 2 like this:

2⁴ = 16
2³ is: 16 divide by 2 = 8
2² is: 8 divide by 2 = 4
2¹ is: 4 divide by 2 = 2
2⁰ is: 2 divide by 2 = 1
Now you have 2⁰ = 1

So from the pattern above when we get to 2⁰ it becomes 2 divide by 2 = 1.

If math is taught this way from the start, it becomes much easier to use formulas later, because students will understand what the formulas are actually doing instead of just memorising formulas

MindHacker9009:
Updated:

Here is a simpler answer a layman can understand, by showing it as a pattern.

2⁴ = 16
2³ = 8
2² = 4
2¹ = 2

Notice the pattern that as it goes down one raise to the power of the number or (go down one exponent) that you're dividing by 2 like this:

2⁴ = 16
2³ is: 16 divide by 2 = 8
2² is: 8 divide by 2 = 4
2¹ is: 4 divide by 2 = 2
2⁰ is: 2 divide by 2 = 1
Now you have 2⁰ = 1

So from the pattern above when we get to 2⁰ it becomes 2 divide by 2 = 1.

If math is taught this way from the start, it becomes much easier to use formulas later, because students will understand what the formulas are actually doing instead of just memorising formulas

Interesting, so everyone was wrong but your answer was the most correct.
Your explanation is very wrong and incorrect. And even unnecessary.

What is 16 doing in 2^3?


Any ways 0 raised to the power of Zero(0^0) renders your explanation invalid.

TheVillian:
Interesting, so everyone was wrong but your answer was the most correct.
Your explanation is very wrong and incorrect. And even unnecessary.

What is 16 doing in 2^3?

Any ways 0 raised to the power of Zero(0^0) renders your explanation invalid.

My method is correct and the simplest explanation.

You asked what is 16 doing in 2^3? It is to show the pattern dropping down from 2⁴ = 16
2³ is: 16 divide by 2 = 8

0⁰ depends on the context unlike 2⁰.
0⁰ In Pure Mathematics or real analysis, is often left undefined, so comparison doesn't make sense here.

But in Combinatorics, Discrete Mathematics, Computer Science and Programming 0⁰ is also defined as 1, for consistency and to avoid errors in code relying on exponentiation rules

MindHacker9009:
My method is correct and the simplest explanation.

You asked what is 16 doing in 2^3? It is to show the pattern dropping down from 2⁴ = 16
2³ is: 16 divide by 2 = 8

0⁰ depends on the context unlike 2⁰.
0⁰ In Pure Mathematics or real analysis, is often left undefined, so comparison doesn't make sense here.

But in Combinatorics, Discrete Mathematics, Computer Science and Programming 0⁰ is also defined as 1, for consistency and to avoid errors in code relying on exponentiation rules

I'm not here to argue sir. Let the readers be the judge

MindHacker9009:
My method is correct and the simplest explanation.

You asked what is 16 doing in 2^3? It is to show the pattern dropping down from 2⁴ = 16
2³ is: 16 divide by 2 = 8

0⁰ depends on the context unlike 2⁰.
0⁰ In Pure Mathematics or real analysis, is often left undefined, so comparison doesn't make sense here.

But in Combinatorics, Discrete Mathematics, Computer Science and Programming 0⁰ is also defined as 1, for consistency and to avoid errors in code relying on exponentiation rules

Your method is the most confusing of all... Trying to explain by bringing 16 to 2 raises to the power 3

MindHacker9009:
The answers so far are the reason many people run away from math, thinking it's hard when in fact, it's very easy if explained in layman's terms, that even a primary six year old can understand

By the way, who told you maths is very easy? Did you mean secondary school maths?

Do you know there are some maths questions unsolved for many decades?

Aydot99:
Your method is the most confusing of all... Trying to explain by bringing 16 to 2 raises to the power 3

Your comment is the one that is very confusing

TheVillian:
By the way, who told you maths is very easy? Did you mean secondary school maths?

Do you know there are some maths questions unsolved for many decades?

Those math that are yet unsolvable can only be found at msc to phd research level. the maths to bsc are all solvable and the challenge I posted can be found a top primary school at level six, for others at early secondary school level.

2^0=2^(1-1)=2¹÷2¹=2÷2=1
.: 2⁰ =1

eastOFwest:
Na all these things wein oyinbo take confuse us. When we cram and memorise all these theories, come pour am out for various exams, we go think say we get sense. Oyinbo go pat us for back, give us Prof. We go dey proud, dey boast say we get highest number of this or that blah blah blah. Ordinary electricity problem we no fit solve.