Question

Can you please explain to me why any number to the power of 0 will always equal one? This 8th grade math is beating me

Answer 1

did u mean :
prove \[x^0=1\]

Answer 2

I need to explain it to a 12 year old - I don't get it...

Answer 3

actually i am also of the same age

Answer 4

ok let me explain wait for a minute

Answer 5

it's been a long time since I was in school! I've forgotten a lot

Answer 6

You can only prove it using the rules of algebra. Kushashwa, just remember you're not average.

Answer 7

i know that i am weak in maths hero ... i am trying to improve atelast upto average level

Answer 8

this site has lead me to from weakest level to atleast weak level .. i am improving i think

Answer 9

I meant that you're above average

Answer 10

oh thanks

Answer 11

ok, but I still don't understand why any number to the power of 0 will always = 1

Answer 12

hmn
i think this can be the proof
see
u know that
1 = a^n / a^n
1= a^(n-n) = a^0
a^0 = 1
hence a^0 = 1

Answer 13

That won't mean anything to a twelve year old

Answer 14

or a 38 y/o either lol

Answer 15

It was a good attempt though

Answer 16

You would have been better off using actual numbers

Answer 17

yes a very good attempt...

Answer 18

but it's not making sense to me

Answer 19

1 * 4 * 4 * 4 = 4^3

1* 4 * 4 = 4^2

1 * 4 = 4^1

Therefore, 1 = 4^0

Answer 20

Since...
x^a*x^b=x^(a+b) --------------- laws of exponents
hence
x^a*x^0=x^(a+0)=x^a

if x^a*x^0=x^a then, x^0 is a multiplicative identity, and must be equal to 1.

Answer 21

this is the easiest one
hero is this right ?

Answer 22

@Tyler that is just a pattern not a proof i think that

Answer 23

kush, you're focusing too much on proving, rather than explaining

Answer 24

Thats the most non-technical way i can think of explaining it

Answer 25

Kush had it with his very first explanation. He just needs to use numbers and explain each step.

Answer 26

so finally this is the proof
Since...
x^a*x^b=x^(a+b) --------------- laws of exponents
hence
x^a*x^0=x^(a+0)=x^a

if x^a*x^0=x^a then, x^0 is a multiplicative identity, and must be equal to 1.
EXPLANATION :
\[x^a * x^b = x^{(a+b)} \]
put x^0 at the place of x^b
\[x^a * x^0 \]
\[x^a * x^0 = x^{(a+0)} = x^a\]
multiplicative identity is the identity which when multplied to any number the answer is the number itself
hence here x^0 is the multplicative identity since it is multiplied to x^a and the result is the same x^a
Multiplicative identity is 1 but here it is x^0 that implies that x^0 = 1

Answer 27

i hope this is sufficient for explaining a 12 year average child

Answer 28

thank you

Answer 29

my pleasure

Answer 30

\[1 = \frac{2^2}{2^2}\] When you are dividing numbers with exponents you subtract the top exponent from the bottom exponent. so \[1 = 2^{2-2}\] so \[1 = 2^0\] This is what kush originally said but i used numbers instead of letters to make the explination clearer

Answer 31

Good tyler....and kush as well.

I think a 12 year old can understand that. Once he does, then you can introduce the more general proof.

Answer 32

Thank you both - Tyler that helps so much!!!!

Answer 33

yea u r right
good tyler also