Evaluate \begin{align*}
\left(c^c-c(c-1)^c\right)^c
\end{align*} when $c=3$.
To evaluate this expression, I need to plug in $c=3$ and simplify using the order of operations. First, I replace every $c$ with $3$: \begin{align*}
\left(3^3-3(3-1)^3\right)^3
\end{align*} Next, I apply the exponent rules inside the parentheses: \begin{align*}
\left(27-3(2)^3\right)^3
\end{align*} \begin{align*}
\left(27-3(8)\right)^3
\end{align*} \begin{align*}
\left(27-24\right)^3
\end{align*} Then, I simplify the subtraction inside the parentheses: \begin{align*}
\left(3\right)^3
\end{align*} Finally, I evaluate the cube of 3: \begin{align*}
27
\end{align*} 