[Tex/LaTex] Problem with \frac macro

Question

I am using this code for a mathematics problem. The code works but the lower fraction looks really dull, the parenthesis is doing something it isn't supposed to. What I can do about this?

\begin{align}
D &= \sum_{i}^{k}\frac{n_i}{\frac{A}({\Delta\sigma_i})^m} \nonumber \\
D &= \sum_{i}^{k}\frac{n_i}{\frac{A}({r_i*\Delta\sigma_{max}})^m} \nonumber \\
D &= \frac{(\Delta\sigma_{max})^m}{A} \sum_{i}^{k}\frac{n_i}{(r_i)^m} \nonumber \\
D &= \frac{(\Delta\sigma_{max})^m}{A} * C \label{eq:constant}
\end{align}

Answer 1

Here's an alternative presentation to avoid fractions within fractions. EDITED to reflect clarified intent of the OP in the comment section.

Also, use \max instead of max, since it is a function.

REEDITED to take Mico's suggestion of using \cdot rather than the *. That is, perhaps, assuming something on the intent of the OP, but it seems a reasonable assumption.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
D &= \sum_{i}^{k}n_i\cdot\frac{({\Delta\sigma_i})^m}{A}\nonumber \\
D &= \sum_{i}^{k}n_i\cdot\frac{({r_i\cdot\Delta\sigma_{\max}})^m}{A} \nonumber \\
D &= \frac{(\Delta\sigma_{\max})^m}{A} \sum_{i}^{k}\frac{n_i}{(r_i)^m} \nonumber \\
D &= \frac{(\Delta\sigma_{\max})^m}{A}\cdot C \label{eq:constant}
\end{align}
Here is what you had:
\begin{align}
D &= \sum_{i}^{k}\frac{n_i}{\frac{A}({\Delta\sigma_i})^m} \nonumber \\
D &= \sum_{i}^{k}\frac{n_i}{\frac{A}({r_i*\Delta\sigma_{max}})^m} \nonumber \\
D &= \frac{(\Delta\sigma_{max})^m}{A} \sum_{i}^{k}\frac{n_i}{(r_i)^m} \nonumber \\
D &= \frac{(\Delta\sigma_{max})^m}{A} * C \label{eq:constant}
\end{align}
\end{document}