\part{Complex expressions}

\begin{definition}
An \emph{expression} is a a 'math sentence' of numbers joined together by operations, that equals a single number when calculated.
\end{definition}

\chapter{Order of operations}

Some complicated expressions have multiple different operators in them, and we have to make a choice on which operation to calculate first. Unfortunately, the order in which we calculate each operation can change our answer. 

\begin{example}
5+7 \times 3 = 5+21 = 26
5+7 \times 3 = 13\times 3 = 39
\end{example}
Us humans need to make our own rules to decide what order we should do our operations. Our answer is the \emph{BODMAS} technique.
\begin{itemize}
	\item Brackets
	\item Orders (powers, roots; more on these later)
	\item Division and Multiplication
	\item Subtraction and Addition
\end{itemize}



\chapter{Exponentiation}

In addition to the field of real numbers, one may wish for a set of rules for squaring, cubing, and other indices. These operations are examples of \emph{exponentiation}; repeated multiplication. These rules can be added as a 'side dish' for our field of real numbers.

- right-distributive over multiplication 
\[\frac{(3+4)}{5}=\frac{3}{5}+\frac{4}{5}\]
- right-distributive over division 
\[\frac{(3-4)}{5}=\frac{3}{5}-\frac{4}{5}\]