symplify the following expression
(3z)with exponent 0
Is the 3z in parenthesis and the 0 is outside that? Or is the exponent 0 only for the z? It will make a difference, but I'll explain how to do it and hope you can understand.
Let's work backwards. Let's start with what exponents do. If you have:
2^2 that is 2 multiplied by itself 2 times. So 2x2.
If you have 2^3, that is 2 multiplied by itself 3 times, or:
2 x 2 x 2
2^4 = 2x2x2x2 (2 multiplied by itself four times) and so on.
To understand 2^0, let's work backwards. We know that multiplication and division are REALLY closely related. So here, if we are multiplying when the numbers go up, we can divide when the numbers go down.
2^4 = 2x2x2x2, or 16.
2^3 = 2x2x2x2 (which is 2^4) DIVIDED BY 2. (That takes away one of the twos and we are left with 2x2x2, or 8.
2^2 = 2x2x2 (which is 2^3) DIVIDED BY 2. That makes it 2x2.
2^1 = 2x2 (which is 2^2) DIVIDED BY 2. That makes it simply 2.
2^0 = 2 (which is 2^1) DIVIDED BY 2...which is one.
"Wait, Matt!" (You say). For ANY number we take and divide by itself, it will ALWAYS be one!
"AHA!" I reply. Any number divided by itself IS always one. Hence, if we try this with any number, we will see:
5^0 = 1
10^0 = 1
10004932489230489239048239024905887623409889980234098234^0 = 1
So now you know the secret to the zero exponent. The only question that remains is my first one on whether there are parenthesis or not.
If there are, and the 0 is OUTSIDE the parenthesis, it means that total answer is one.
If there isn't and it's next to the z, it means 3 x z^0 (or...3x1)
Hope this helped and it makes sense.