Algebra-practice-computing-with-exponents.tex

\Section{Algebra practice---exponents}
\Subheading{Computing}

Evaluate each of these expressions by hand.
Your result should be an integer or a fraction in lowest terms.
Throughout this section, use a calculator to check your work \emph{after} trying each problem.
Be sure you're entering expressions like these into the calculator correctly.

{
 \renewcommand{\arraystretch}{3.5}
 \large
 \begin{tabular}{>{$}p{3in}<{$}>{$}p{3in}<{$}}
   2^4 =     & \pfrac{1}{2}^4 =\\
   2^3 =     & \pfrac{1}{2}^3 =\\
   2^2 =     & \pfrac{1}{2}^2 = \\
   2^1 =     & \pfrac{1}{2}^1 = \\
   2^0 =     & \pfrac{1}{2}^0 = \\
   2^{-1} =  & \pfrac{1}{2}^{-1} = \\
   2^{-2} =  & \pfrac{1}{2}^{-2} = \\
   2^{-3} =  & \pfrac{1}{2}^{-3} = \\
   2^{-4} =  & \pfrac{1}{2}^{-4} =\\
 \end{tabular}
}

\newpage

Use decimal notation for fractions on this page.

{
 \renewcommand{\arraystretch}{3.5}
 \large
 \begin{tabular}{>{$}p{3in}<{$}>{$}p{3in}<{$}}
   10^4 =     & 0.1^4 =\\
   10^3 =     & 0.1^3 =\\
   10^2 =     & 0.1^2 = \\
   10^1 =     & 0.1^1 = \\
   10^0 =     & 0.1^0 = \\
   10^{-1} =  & 0.1^{-1} = \\
   10^{-2} =  & 0.1^{-2} = \\
   10^{-3} =  & 0.1^{-3} = \\
   10^{-4} =  & 0.1^{-4} =\\
 \end{tabular}
}

\newpage

Express each of these as an integer or a fraction in lowest terms.

\begin{multicols}{2}

 \begin{ProblemSet}[pencil space=1in]
  \EqProb{-2^{-1}}
  \EqProb{(-2)^{-1}}

  \EqProb{0^2}
  \EqProb{0^1}
  \EqProb{0^0}
  \EqProb{0^{-1}}

  \EqProb{1^2}
  \EqProb{1^1}
  \EqProb{1^{-1}}
  \EqProb{-1^2}
  \EqProb{(-1)^2}
  \EqProb{(-1)^3}

  \EqProb{-2^2}
  \EqProb{-(2^2)}
  \EqProb{(-2)^2}
  \EqProb{-2^3}
  \EqProb{-(2^3)}
  \EqProb{(-2)^3}
  \EqProb{-2^{-2}}
  \EqProb{-(2^{-2})}
  \EqProb{(-2)^{-2}}
  \EqProb{-2^{-3}}
  \EqProb{-(2^{-3})}
  \EqProb{(-2)^{-3}}

  \EqProb{\pfrac{1}{2}^{-1}}
  \EqProb{-\pfrac{1}{2}^{-1}}
  \EqProb{\left(-\pfrac{1}{2}\right)^{-1}}
 \end{ProblemSet}
\end{multicols}

\newpage

Express each of these as ten to an integer power.

\bigskip
\begin{multicols}{2}
 \begin{ProblemSet}[pencil space=1in]
  \EqProb{0.01^2}
  \EqProb{-0.01^3}
  \EqProb{(-0.1)^{-3}}
  \EqProb{0.01^{-2}}
  \EqProb{-0.01^{-2}}
  \EqProb{(-0.01)^{-3}}
  \EqProb{10 \times 10}
  \EqProb{100 \times 0.1}
  \EqProb{0.1 \times 0.1}
  \EqProb{\frac{1}{0.1}}
  \EqProb{\frac{0.1}{0.1}}
  \EqProb{\frac{10}{0.1}}
  \EqProb{\frac{0.001}{100}}
 \end{ProblemSet}
\end{multicols}

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