maths, algebra

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.

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  1. 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

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  2. 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]).

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  3. 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.

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  4. 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^(5-2)

    That is, when you divide powers, you subtract exponents.

    So, x^5 / x^5 = 1, but
    it is also x^(5-5) = x^0

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  5. sorry about the typos:
    x^5/x^2 = (x*x*x*x*x)/(x*x) = x*x*x = x^3 = x^(5-2)

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  6. can you show me the work for my homework

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  7. so 3 has a power of zero, correct?

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