Adding Powers of 9

Number Theory Level 1

\[\begin{array}{rcccr} {\color{red}9^0}+9^1 & = & {\color{red}1}+9 & = & {\color{red}1}0 \\ {\color{red}9^1}+9^2 & = & {\color{red}9}+81 & = & {\color{red}9}0 \\ {\color{red}9^2}+9^3 & = & {\color{red}81}+729 & = & {\color{red}81}0 \\ \end{array}\]

Is the following true for any positive integer \(n?\) \[{\color{red}9^n}+9^{n+1}={\color{red}9^n} \times 10\]