My question is relating to Mathematics exponential functions.?
If 3 to the power of 2 is 3 x 3 which is equal to nine and 3 to the power of 1 is 3 x 1 (I think) which is equal to 3, why is 3 to the power of 0 equal to 1? What's the explanation for this?
Answers:
Since any number to the power of 0 is one, then let us take x to the power of zero and see how it come out to be 1.
X^0 is = X^1 * X^-1
X^0 = X^1/X^1
X^0 is equal X^1 /X^1which is x/x = 1
X^0 =1 no matter what the value of X is!
well its all french to me
A famous mathematician once quote "In mathematics you dont have to understand. You just have to get used to it"
i do not know yet but i will tell u in 3 days so keep in touch with me
hey look at this website and scroll down and it should help you
http://regentsprep.org/regents/mathb/4b1.
Plot a graph of 3^x (or anything else to the power x) and it has to cross the Y-axis (x=0 on the Y-axis) at y=1.
3 to the power of 2 is written as
3^2
so 'x' to the power of 'a' is written as
x^a
where 'x' and 'a' are any number you want.
So,
3^3 = 3 x 3 x 3 (multiply 3 three times)
3^2 = 3 x 3 (multiply 3 two times)
3^1 = 3 (multiply 3 one time)
3^a = multiply 3 'a' times (for whatever 'a' is)
3^0 = ? (multiply 3 zero times)
The question is really deep and it has to do with continuity. You see, we went from a=3 to a=2 to a=1 but why not a=1.4 or a=0.3?
Not so easy to calculate (and needless to say it doesn't fit the "multiply 3 some many times" formula) but in higher math it will be needed so what you do to figure out what 3^0 is you start with 3^a and calculate it for a=1 then a=0.1 then a=0.01 and keep going. Eventually you realize that as a gets smaller and smaller the result gets closer and closer to 1.
Hope I didn't confuse you and !Good Question!
-jose-
The answer deals with the mathematical laws of exponents. Here is a great explanation found at Dr. Math:
http://mathforum.org/dr.math/faq/faq.num.
It makes sense, really.
First, do you see that x^a * x^b = x^(a + b) ?
For instance, 2^3 * 2^5 = 2*2*2 * 2*2*2*2*2 = 2^8
So, for nonzero x, x^y * x^0 = x^(y + 0) = x^y
If x^y * x^0 = x^y, then divide by x^y to get x^0 == 1 for all nonzero x
This is a bit complicated to explain. here is a link that spells it out in detail:
http://www.math.com/school/subject2/less.
OK, 3 squared is nine, right?
Well, three to the NEGATIVE two is one over nine or one ninth.
It's accepted that when multiplying terms you can add and subtract exponents of the same base. in this case three.
So, 3 squared multiplied by 3 to the negative two would be the same as nine times one ninth, or nine over nine. anything over itself is one! Also, two plus negative two is zero. for the zero exponent.
Does that help?
3^(2)= 3*3 =9
3^(2-2) = 3^(0) =3^(2)/3^(2) = 9/9=1
in general,
x^(a-a) =x^(0) = x^(a)/x^(a) =1
i hope that this helps
Everything raised to the power of zero is 1, except for zero itself. Zero to the power of zero is undefined, but in certain situations like power series of which e is, zero to the power of zero is treated as 1.
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Answers:
Since any number to the power of 0 is one, then let us take x to the power of zero and see how it come out to be 1.
X^0 is = X^1 * X^-1
X^0 = X^1/X^1
X^0 is equal X^1 /X^1which is x/x = 1
X^0 =1 no matter what the value of X is!
well its all french to me
A famous mathematician once quote "In mathematics you dont have to understand. You just have to get used to it"
i do not know yet but i will tell u in 3 days so keep in touch with me
hey look at this website and scroll down and it should help you
http://regentsprep.org/regents/mathb/4b1.
Plot a graph of 3^x (or anything else to the power x) and it has to cross the Y-axis (x=0 on the Y-axis) at y=1.
3 to the power of 2 is written as
3^2
so 'x' to the power of 'a' is written as
x^a
where 'x' and 'a' are any number you want.
So,
3^3 = 3 x 3 x 3 (multiply 3 three times)
3^2 = 3 x 3 (multiply 3 two times)
3^1 = 3 (multiply 3 one time)
3^a = multiply 3 'a' times (for whatever 'a' is)
3^0 = ? (multiply 3 zero times)
The question is really deep and it has to do with continuity. You see, we went from a=3 to a=2 to a=1 but why not a=1.4 or a=0.3?
Not so easy to calculate (and needless to say it doesn't fit the "multiply 3 some many times" formula) but in higher math it will be needed so what you do to figure out what 3^0 is you start with 3^a and calculate it for a=1 then a=0.1 then a=0.01 and keep going. Eventually you realize that as a gets smaller and smaller the result gets closer and closer to 1.
Hope I didn't confuse you and !Good Question!
-jose-
The answer deals with the mathematical laws of exponents. Here is a great explanation found at Dr. Math:
http://mathforum.org/dr.math/faq/faq.num.
It makes sense, really.
First, do you see that x^a * x^b = x^(a + b) ?
For instance, 2^3 * 2^5 = 2*2*2 * 2*2*2*2*2 = 2^8
So, for nonzero x, x^y * x^0 = x^(y + 0) = x^y
If x^y * x^0 = x^y, then divide by x^y to get x^0 == 1 for all nonzero x
This is a bit complicated to explain. here is a link that spells it out in detail:
http://www.math.com/school/subject2/less.
OK, 3 squared is nine, right?
Well, three to the NEGATIVE two is one over nine or one ninth.
It's accepted that when multiplying terms you can add and subtract exponents of the same base. in this case three.
So, 3 squared multiplied by 3 to the negative two would be the same as nine times one ninth, or nine over nine. anything over itself is one! Also, two plus negative two is zero. for the zero exponent.
Does that help?
3^(2)= 3*3 =9
3^(2-2) = 3^(0) =3^(2)/3^(2) = 9/9=1
in general,
x^(a-a) =x^(0) = x^(a)/x^(a) =1
i hope that this helps
Everything raised to the power of zero is 1, except for zero itself. Zero to the power of zero is undefined, but in certain situations like power series of which e is, zero to the power of zero is treated as 1.
The answers post by the user, for information only, UKQnA.com does not guarantee the right.