Exponents in the denominator? I'm having trouble understanding exponents in the denominator.
For example: I have the expression: $\displaystyle 1 - \frac{1}{3^n} + \frac{2}{3^{n+1}}$.
I know that this simplifies to $\displaystyle 1 - \frac{1}{3^{n+1}}$, but how/why? Can someone please list the steps?
My understanding is that the exponent $(n+1)$ in the expression $x^{n+1}$ means that $x^{n+1} = x x^n$, but how does this fit with the above problem?

You should get a common denominator for the last two terms by multiplying the second term by $3/3$. You have
$$
\begin{align*}
1-\frac{1}{3^n}+\frac{2}{3^{n+1}} &= 1-\frac{3}{3^{n+1}}+\frac{2}{3^{n+1}}\\
&= 1-\frac{1}{3^{n+1}}
\end{align*}
$$
