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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Yes, it can be applied in any case. First, let's define exponentiation. $\displaystyle a^0 = 1 \ a^1 = a \ a^2 = a^1 \cdot a^1 \ a^3 = a^2 \cdot a^1 $ $\displaystyle a^{n+1} = a^n \cdot a^1 $ is the very definition of integer exponentiation.
Originally Posted by kapital 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 $\displaystyle y^{n+1}=y^ny$ for $\displaystyle y=4$ Your second example is $\displaystyle y^{n+1}=y^ny$ for $\displaystyle y=x+1$
Originally Posted by kapital 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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