why is:
0
350
350 to the power of zero 1?
why is 350 to the power of 0 equal to 1?? ?
2008-09-02 11:43 am
回答 (9)
2008-09-02 11:48 am
✔ 最佳答案
a^n × a^m = a^(n+m)a^n / a^m = a^(n-m)
If n=m
a^n / a^n = a^(n-n)
a^0 = 1 for all non-zero values of a
350^0 = 1
2008-09-02 11:49 am
a^m/a^m=1
Also a^m/a^m=a^(m-m)=a^0
so a^0=1
Also a^m/a^m=a^(m-m)=a^0
so a^0=1
2008-09-02 11:55 am
Any nonzero number raised to the 0 power is 1.
One way to think of this is that raising to whole number powers
is multiplying the numbers that number of times.
350^1 = 350
350^2 =350 X 350
and
350^3=350 X 350 x 350
Now we know that any number times 1 equals itself
so we can write
350^1 = 1 x 350
350^2 = 1 X 350 X 350
and
350^3= 1 x 350 X 350 x 350
Now
350^0 = 1 {not multiplied by any 350's at all}
so it is just 1
Moreover we need for 350^0 to equal 1 if our rules for exponents are to
hold when we move to negative exponents.
350^ -1 = 1/350
and 350^-1 x 350^1 = 350^0
and that is (1/350) X 350 = 1
One way to think of this is that raising to whole number powers
is multiplying the numbers that number of times.
350^1 = 350
350^2 =350 X 350
and
350^3=350 X 350 x 350
Now we know that any number times 1 equals itself
so we can write
350^1 = 1 x 350
350^2 = 1 X 350 X 350
and
350^3= 1 x 350 X 350 x 350
Now
350^0 = 1 {not multiplied by any 350's at all}
so it is just 1
Moreover we need for 350^0 to equal 1 if our rules for exponents are to
hold when we move to negative exponents.
350^ -1 = 1/350
and 350^-1 x 350^1 = 350^0
and that is (1/350) X 350 = 1
2008-09-02 11:49 am
eg.)
350^2 ÷ 350^2
= 350^(2 - 2) [= (35 x 35) ÷ (35 x 35)]
= 350^0 [= 122500 ÷ 122500]
= 1
∴ 350^0 = 1
350^2 ÷ 350^2
= 350^(2 - 2) [= (35 x 35) ÷ (35 x 35)]
= 350^0 [= 122500 ÷ 122500]
= 1
∴ 350^0 = 1
2008-09-02 11:49 am
IT HAS TO DO WITH THE NUMBER OF TACOS YOU ATE LAST NIGHT!
2008-09-02 12:33 pm
350^0 (350 to the power of 0) = 1 because it is by definition that any nonzero number to the power 0 is 1.
a ≠ 0 , a^0 = 1
This definition was introduced to expand the domain of application of the rules of exponentiation.
For example, a well known property of positive integer exponents is
a ≠ 0, a^m/a^n = a^(m-n)
with m and n being 2 positive integers and m>n.
Now, what happens if m = n?
If m = n, a^m/a^n = 1 and a(m-n) = a^0
For this reason one define a^0 = 1
a ≠ 0 , a^0 = 1
This definition was introduced to expand the domain of application of the rules of exponentiation.
For example, a well known property of positive integer exponents is
a ≠ 0, a^m/a^n = a^(m-n)
with m and n being 2 positive integers and m>n.
Now, what happens if m = n?
If m = n, a^m/a^n = 1 and a(m-n) = a^0
For this reason one define a^0 = 1
2008-09-02 12:06 pm
anything to the power of 0 is 1 and only 1
2008-09-02 11:48 am
Why is 1 to the power of 0, 1? Or why is 2 to the power of 0, 1? Similarly 350 to the power of 0 is 1. It is a property you cant question it!
2008-09-02 11:46 am
Because anything to the power of zero is 1, just as anything to the power of one is itself
參考: Algebra 2
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