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\def\headlineaux{\sc Math 101: Algebra for College Students
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\begin{titlepage}\begin{centerline}{\Huge \framebox{Burton Rosenberg}}
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\section*{Test 4 \hfill{\parbox{3in}
    {\small\sc\begin{flushright} July 19, 1996.
\end{flushright}}}}

There are 15 problems. You have until 9:55. (1 hr. and 25 min.)
\begin{enumerate}
\item
Rewrite this expression using only positive exponents and simplify:
\[ (-4y^{-3}z)^{-3} \]
\item
Rewrite this expression using only positive exponents and simplify:
\[ (5s^5t^{-5})\left({ 3s^{-2}\over 50t^{-1}}\right)\]
\item
Rewrite this expression using only positive exponents and simplify:
\[{ u^{-1} - v^{-1} \over u^{-1} + v^{-1}} \]
\item
Is this number rational:
\[ \sqrt{ {9 \over 16 }}\]
\item
Is this number rational:
\[ \sqrt{72} \]
\item
Perform the indicated multiplication:
\[ x^{4/3}\bigl( 3x^2 - 4x + 5 \bigr) \]
\item
Perform the indicated multiplication:
\[ ( x^{1/2} -3)(x^{1/2}+3) \]
\item
What is the domain of this expression:
\[ \sqrt{4x^3} \]
\item 
Combine radical expressions:
\[{2\over 5}\sqrt{5} - {6\over 5}\sqrt{5}\]
\item
Combine these radicals:
\[ 9\sqrt[3]{17} + 7\sqrt[3]{2} - 4\sqrt[3]{17} + \sqrt{2}\]
\item
Combine these radicals:
\[3\sqrt{x+1} + 10\sqrt{x+1}\]
\item
The period $T$ in seconds of a pendulum is given by:
\[ T = 2 \pi \sqrt{ L \over 32 } \]
where $L$ is the length of the pendulum in feet. Find the
period of a pendulum whose length is 8 feet.
\item
Which is larger, $\sqrt{10}-\sqrt{6}$ or $\sqrt{10-6}$.
\item
Rationalize the denominator of this expression:
\[ 10 \over \sqrt{9} + \sqrt{5} \]
\end{enumerate}
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