simplifying exponents worksheet

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For inline formulas, enclose the formula in $…$. For displayed formulas, use $$…$$. Here is an example of an inline formula: $x^2 + y^2 = z^2$.

\section{Numbering and referencing}

For any real number $x$, we have \begin{align}\exp (ix)& =\sum _{k=0}^{\infty }{\frac {(ix)^{k}}{k!}}\label{eq:1}\\ & = \cos x+i\sin x.\label{eq:2}\end{align} The equation \eqref{eq:1} is the power series definition of the exponential function, and the equation \eqref{eq:2} is known as Euler’s formula.

\section{Theorem environment} \begin{theorem}[Fermat's Last Theorem]\label{thm:fermat} No three positive integers $a$, $b$, and $c$ satisfy the equation $a^n + b^n = c^n$ for any integer value of $n$ greater than $2$. \end{theorem}

Fermat’s lost proof. I have a proof of this theorem, but there is not enough space. ◻


Einstein’s journal paper (Einstein 1905) and Dirac’s book (Dirac 1981) are physics-related items.

Dirac, Paul Adrien Maurice. 1981. The Principles of Quantum Mechanics. International Series of Monographs on Physics. Clarendon Press.
Einstein, Albert. 1905. Zur Elektrodynamik bewegter Körper. (German) [On the Electrodynamics of Moving Bodies].” Annalen Der Physik 322 (10): 891–921.

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