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Math Help - exponents

  1. #1
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    exponents

    I now that 4^(n+1) is the same as4^(n)*4.

    But can this mathematical law be applied in any case?

    For example is also true (x+1)^(n+1)=(x+1)^(n)*(x+1)?
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  2. #2
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    Yes, it can be applied in any case. First, let's define exponentiation.

     a^0 = 1 \ a^1 = a \ a^2 = a^1 \cdot a^1 \ a^3 = a^2 \cdot a^1

     a^{n+1} = a^n \cdot a^1 is the very definition of integer exponentiation.
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  3. #3
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    Quote Originally Posted by kapital View Post
    I know that 4^(n+1) is the same as 4^(n)*4.

    But can this mathematical law be applied in any case?

    For example is also true (x+1)^(n+1)=(x+1)^(n)*(x+1)?
    Your first example is

    y^{n+1}=y^ny for y=4

    Your second example is

    y^{n+1}=y^ny for y=x+1
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  4. #4
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    Quote Originally Posted by kapital View Post
    For example is also true (x+1)^(n+1)=(x+1)^(n)*(x+1)?
    Well, assign a value to x and n and try it out...
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