Adding Powers of 9

$\begin{array}{rcccr} {\color{#D61F06}9^0}+9^1 & = & {\color{#D61F06}1}+9 & = & {\color{#D61F06}1}0 \\ {\color{#D61F06}9^1}+9^2 & = & {\color{#D61F06}9}+81 & = & {\color{#D61F06}9}0 \\ {\color{#D61F06}9^2}+9^3 & = & {\color{#D61F06}81}+729 & = & {\color{#D61F06}81}0 \\ \end{array}$

Is the following true for any positive integer $n?$ ${\color{#D61F06}9^n}+9^{n+1}={\color{#D61F06}9^n} \times 10$