# exponents

• Feb 10th 2011, 11:13 AM
kapital
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)?
• Feb 10th 2011, 11:39 AM
Rabolisk13
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.
• Feb 10th 2011, 01:30 PM
Quote:

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)?

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

$y^{n+1}=y^ny$ for $y=x+1$