How come if a number has the written exponent of ''0'' its exponent is seen as ''1''?

Question

if you dont understand what im saying let me try to write it out, the exponents will be in perentheses.

5(4) x 5(0) = 5(5)

i dont really know how to further explain, i hope you understand

Answer 1

First off... I will use ^ to denote exponentation. THat is, 5 to the 3rd power will be denoted by 5^3.

Now on to the heart of the problem.

5^4 * 5^0 is NOT 5^5.

Remember that any nonzero number to the zeroth power is 1. That is, 5^0 = 1. The exponent itself is not 1. The number to the zeroth power is 1.

So 5^4 * 5^0 = 5^4 * 1 = 5^4

Answer 2

Actually I think your equation should read (this time with the exponent after the "^"):

5^4 * 5^0 = 5^4

since 5^0 = 1.

the exponent tells you how many of the base number you are multiplying, right? so 5^4 = 5*5*5*5 and 5^1 = 5.
The good question is why do we say 5^0 = 1 (instead of say, zero?). The answer is partly just "that's how we define it".

But if you think about it, it makes sense. In the equation above, when you multiply two numbers with exponents (of the same base), you ADD the exponents
5^4 * 5^1 = 5*5*5*5 * 5 = 5^5

So, defining 5^0 = 1 is the only way to make the original equation work out.

Answer 3

Your equation is incorrect.

5^4 x 5^0 = 5^4 because 5^0=1.

Anything raised to the 0 power is equal to 1.
as an eqample to show why: If you simplify y^2/y^2 you get 1 by canceling like terms on the top and bottom...or you can move the bottom term (denominator) to the top (numerator) and change the exponent to negative (y^2 x y^-2). When you perform this multiplication you now have y^0. Therefore, y^0=1.

Answer 4

I do not think that due to the fact that y^2/y^2 =1 and by writing y^2/y^2 in the form y^(2-2)
we can derive the equation y^0 =1.
y^n/y^n =1 and y^0 =1 are two equivalent equations, one is needed to prove the other.
But y^0=1 is taken by convention.
The mathematics( not only the number operations )
in general agree that y^0 should be 1 as long as y is not 0.

Answer 5

Your example is not even correct because 5^0 = 1, so that question would be 5^4, not 5^5.

Any number raised to the zero power (except 0) equals 1. Any number raised to the power of one equals itself

Answer 6

Any number, say x to the zero power,
x^0 is by definition, one, unity, 1
If you think about it, it is logical that an number to the power 1 is x^1 or x; so x to the zero or x^(1-1) = x^1/x^1 = 1