Why is anything raised to the 0 power 1 ??

Answer 1

x^a / x^b = x^(a-b)

Now
x^a / x^a = 1
But
x^a / x^a = x^(a-a) = x^0
so
x^0 = 1

Answer 2

Let x be any number; then x^1 = x; but if the exponent is zero, then you are taking that any number 0 times.
Consider the following eqn:
y(x) = q^x where q is any number
Take the natural log of both sides:
ln[y(x)] = ln[q^x] = x ln[q] so that ln[q] is some other number say q'
If in the above eqn x = o, then ln[y] = 0
raise both sides to exp: y = e^0; now look at the graph of e^x and note what happens when x = 0

Answer 3

It is consistent with other mathematical facts e.g.
Line1) 3^5= 343
Line2) 3^4=81
Line3) 3^3 = 27
Line4) 3^2 = 9
Line5) 3^1 = 3
To get from one line to the next, divide the value on the right hand side by 3.
Line6 is 3^0 = 3/3 = 1

Repeat all these steps with 2 or 4 or 5 .... Divide by 2 or 3 or 5 respectively when the time comes. It works.

Answer 4

it is the age old question when anyone envounters it for the first time
it is an identity...it establishes what happens when you take any value raised to this power
think of it as the identity factor 1, anything can be factored by itself and 1...even primes, right?

Answer 5

As the power approaches zero the value of expression approaches one.
Suppose base and exponent then reduce exponent as it approach zero see the value of the expression after rounding off it will definitely be one.

Answer 6

Think about it- squares are the same numbers multiplied together
trips are the same number times 3
so I am going to take this number and multiply it by no other of the same number. Therefore, I have only 1 of that number, thus....

Answer 7

remember the formula a^x /a^y = a^(x-y)
the sign ^ means power
so if in the formula a^x /a^y = a^(x-y), you replace x by y,
you find
a^x /a^y = a^(x-y) --> a^y / a^y = a^(y-y) =a^0 =1