Question

Explain why 1 raised to any power is equal to 1 ?

Answer 1

1^n , means one multiplied n times , however small or large the number be , 1^ any power is always equal to one , even if you consider negative number

Answer 2

what about \(1^{\sqrt2}\) ?

Answer 3

1

Answer 4

:)

Answer 5

yes i know, but it does not conform to your reasoning

Answer 6

\[n \in R\]

Answer 7

since exponentiation is not repeated multiplication
as multiplication is not repeated addition

just being obnoxious, ignore me

Answer 8

:)

Answer 9

i agree, but it is not because "1^n , means one multiplied n times "

Answer 10

ooh , then why is it

Answer 11

that reasoning doesn't even work for \(1^0\)

Answer 12

as you cannot multiply a number by itself zero times

Answer 13

\[\huge x \in R -0\]

Answer 14

Is it the correct domain

Answer 15

i have no idea what that means
what about \(1^{-1}\) or \(1^{\pi}\)

Answer 16

"1^n , means one multiplied n times "
\(\large 1^{\pi}\) means one multiplied \(\pi\) times "?? no meaning there

Answer 17

"1^n , means one multiplied n times "
\(1^{-1}\) means one multiplied \(-1\) times " ?? nope

Answer 18

2^n , means 2 multiplied n times

Answer 19

2^3 = 2*2*2

Answer 20

1^3 = 1*1*1

Answer 21

\(2^{\sqrt2}\) means \(2\) multiplied by itself \(\sqrt2\) times lol

Answer 22

your reasoning only work for \(n\in \mathbb{N}\) not for \(n\in \mathbb{Z}\) or \(n\in\mathbb{Q}\) or \(n\in \mathbb {R}\)

Answer 23

FOR 1^-1
You obviously know this we use indices property
It is weird to imagine that but it is

Answer 24

Yeah , i know , but the dude asking the question , i am presuming he won't all this

Answer 25

@Hahuja Do you also wanta a explaination for why n^0 = 1?

Answer 26

@Adjax
1) by definition ( a not very satisfactory but true answer) unless
2) you can precisely define \(b^x\) for all \(x\in \mathbb{R}\) \(b>0\)

Answer 27

\[\huge 2^{\sqrt{2}}\]
means 2 multiplied by root 2 times

Answer 28

How to multiply a number by root 2 times?

Answer 29

you cannot

Answer 30

yeah you cannot

Answer 31

but its what it is

Answer 32

@satellite73 ..thats all pure math stuff(a college lvl. stuff)..and here the frame of reference is not that high enough

Answer 33

for that matter you cannot even multiply something by itself zero times or two thirds times or minus five times

Answer 34

there's a very good explaination on betterexplained.com by mr.Kalid Azad on this matter from the point of beginner 's view

Answer 35

that is probably true, you resort to "because it is" or "by definition" or "it seems obvious that"...

Answer 36

If you can't how do you calculate it what's the proof

Answer 37

if you want to see why \(2^0\) or \(b^0\) ought to be \(1\) then look at the pattern
\[2^4=16\\
2^3=8\\
2^2=4\\
2^1=2\\
2^0=?\] pretty clear you are diving by \(2\) each time

Answer 38

'what's the proof":

Pursue a degree in pure mathematics/...that will give answer to all yar questions and that will give you a handful of greek letters that why a slice of pizza exists(book way:why a fraction/fractional no. exist?)

Answer 39

that does not prove that it is 1 , but it suggests that 2^0 might be 1

Answer 40

What is the course to take to solve such problems?

Answer 41

here's the link:
http://betterexplained.com/articles/understanding-exponents-why-does-00-1/

Answer 42

if you want to know why \(2^0=1\) other than by definition, what you need to know is that
\[b^x:=e^{x\log(b)}\]

Answer 43

@satellite73 : your above e.h. is not a kind of..err...what about a different no. n instead of 0..

one more link:

http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/

Answer 44

Is the log there the natural log?

Answer 45

there is only one log, but yes

Answer 46

well , to real numbers power its true
try to learn complex :D u will start to see things

Answer 47

and yes your above eqn. reminded me of a EQN> in my fogged memory which proved that for a complex no. Z to the power of real no. N can be evaluated

Answer 48

a number different from zero is just a different number
\[2^\sqrt2=e^{\sqrt2\log(2)}\]

Answer 49

why man invented zero?

Answer 50

REal nos. are subset of complex no..