maths, algebra
posted by AK on .
State the degree of each of the following:
a)3
b)x^0
My answer for a) was: 1
My answer for b) was: 1
BUT
at the back of the book, the answer for a) was 0. The answer for b) was also 0.
I just don't understand why I'm wrong.

all constants have a degree of 0.
x^0 = 1
20 = 20*x^0
10 = 10*x^0
x^0 obviously has degree 0. How did you think it was 1? The power is the degree.
x^1 (or, just x) has degree 1 
well,now that i know that all constants have a degree of zero, i understand.
It's just that, i thought that numbers and variables that have no index are to the power 1; since x^1=x, I thought it would be okay to apply this rule on constants as well.
In a), I thought the degree of 3 was 1 according to the rule: x^1=x (like: 3^1=3, I just thought the index wasn't written)
and in b), I thought that since x^0=1, i had to state the degree of the 1.
And i thought the degree of 1 was 1 until you told me that all constants have a degree of zero (which is something i only just found out about and don't entirely understand [to be honest]). 
cool. Now it's something you don't have to worry about any more. Sometimes you have to pound these concepts in with a hammer. I know; my head still hurts.

the reason why x^0 is 1, can be easily seen, if you have worked with exponents yet:
x^5 = x*x*x*x*x
x^2 = x*x
x^/x^2 = (x*x*x*x*x)/(x*x) = x*x*x = x63 = x^(52)
That is, when you divide powers, you subtract exponents.
So, x^5 / x^5 = 1, but
it is also x^(55) = x^0 
sorry about the typos:
x^5/x^2 = (x*x*x*x*x)/(x*x) = x*x*x = x^3 = x^(52) 
can you show me the work for my homework

so 3 has a power of zero, correct?