In Exercises arithexfirst - arithexlast, perform the indicated operations and simplify.
\(5 - 2 + 3\)

\(6\)

\(5 - (2+3) = \answer {0}\)
\(\frac {2}{3} - \frac {4}{7}\)

\(\frac {2}{21}\)
\(\frac {3}{8} + \frac {5}{12} = \answer {\frac {19}{24}}\)
\(\frac {5-3}{-2-4}\)

\(-\frac {1}{3}\)
\(\frac {2(-3)}{3 - (-3)} = \answer {-1}\)
\(\frac {2(3)-(4-1)}{2^2 + 1}\)

\(\frac {3}{5}\)
\(\frac {4 - 5.8}{2 - 2.1} = \answer {18}\)
\(\frac {1 - 2(-3)}{5(-3) + 7}\)

\(-\frac {7}{8}\)
\(\frac {5(3) - 7}{2(3)^2-3(3)-9}\)

Undefined. (division by \(0\).)
\(\frac {2((-1)^2-1)}{((-1)^2+1)^2} = \answer {0}\)
\(\frac {(-2)^2 - (-2) - 6}{(-2)^2 - 4}\)

Undefined. (division by \(0\).)
\(\frac {3 - \frac {4}{9}}{-2 - (-3)} = \answer {\frac {23}{9}}\)
\(\frac {\frac {2}{3} - \frac {4}{5}}{4 - \frac {7}{10}}\)

\(-\frac {4}{99}\)
\(\frac {2\left (\frac {4}{3}\right )}{1 - \left (\frac {4}{3}\right )^2} = \answer {-\frac {24}{7}}\)
\(\frac {1 - \left (\frac {5}{3}\right )\left (\frac {3}{5}\right )}{1 + \left (\frac {5}{3}\right )\left (\frac {3}{5}\right )}\)

\(0\)
\(\left (\frac {2}{3}\right )^{-5} = \answer {\frac {243}{32}}\)
\(3^{-1} - 4^{-2}\)

\(\frac {13}{48}\)
\(\frac {1 + 2^{-3}}{3 - 4^{-1}} = \answer {\frac {9}{22}}\)
\(\frac {3\cdot 5^{100}}{12 \cdot 5^{98}}\)

\(\frac {25}{4}\)
\(\sqrt {3^2 + 4^2} = \answer {5}\)
\(\sqrt {12} - \sqrt {75}\)

\(-3\sqrt {3}\)
\((-8)^{2/3} - 9^{-3/2} = \answer {\frac {107}{27}}\)
\(\left (-\frac {32}{9}\right )^{-3/5}\)

\(-\frac {3\sqrt [5]{3}}{8} = -\frac {3^{6/5}}{8}\)
\(\sqrt {(3-4)^2 + (5-2)^2} = \answer {\sqrt {10}}\)
\(\sqrt {(2 - (-1))^2 + \left (\frac {1}{2} - 3\right )^2}\)

\(\frac {\sqrt {61}}{2}\)
\(\sqrt {(\sqrt {5} - 2\sqrt {5})^2 + (\sqrt {18} - \sqrt {8})^2} = \answer {\sqrt {7}}\)
\(\frac {-12 + \sqrt {18}}{21}\)

\(\frac {-4 + \sqrt {2}}{7}\)
\(\frac {-2 - \sqrt {(2)^2 - 4(3)(-1)}}{2(3)} = \answer {-1}\)
\(\frac {-(-4) + \sqrt {(-4)^2 - 4(1)(-1)}}{2(1)}\)

\(2 + \sqrt {5}\)
\(2(-5)(-5+1)^{-1} + (-5)^2(-1)(-5+1)^{-2}\)

\(\frac {15}{16}\)
\(3\sqrt {2(4)+1} + 3(4)\left (\frac {1}{2}\right )(2(4)+1)^{-1/2}(2) = \answer {13}\)
\(2(-7)\sqrt [3]{1-(-7)} + (-7)^2 \left (\frac {1}{3}\right )(1-(-7))^{-2/3}(-1)\)

\(-\frac {385}{12}\)
With the help of your calculator, find \((3.14 \times 10^{87})^{117}\). Write your final answer, using scientific notation, rounded to two decimal places. (See Example scientificnotationex.)

\(1.38 \times 10^{10237}\)
Prove the Quotient Rule and Power Rule stated in Theorem radicalprops.
Discuss with your classmates how you might attempt to simplify the following.
  1. \(\sqrt {\frac {1 - \sqrt {2}}{1 + \sqrt {2}}}\)
  2. \(\sqrt [5]{3} - \sqrt [3]{5}\)
  3. \(\frac {\pi + 7}{\pi }\)