Practice with Rational Exponents
These ideas are also explored in these web exercises: Writing Radicals in Rational Exponent Form and Writing Rational Exponents as Radicals.
Here, you will practice simplifying expressions involving rational exponents.
Examples
$\cssId{s9}{9^{1/2}}
\cssId{s10}{= \sqrt{9}}
\cssId{s11}{= 3}$
$\cssId{s12}{(-9)^{1/2}}
\cssId{s13}{= \sqrt{-9}}
\cssId{s14}{= \text{nd}}$
Input ‘nd’ if an expression is not defined.
Input ‘nd’ if an expression is not defined.
$\cssId{s16}{-9^{1/2}}
\cssId{s17}{= -\sqrt{9}}
\cssId{s18}{= -3}$
$\displaystyle
\cssId{s19}{9^{-1/2}}
\cssId{s20}{= \frac{1}{9^{1/2}}}
\cssId{s21}{= \frac{1}{\sqrt{9}}}
\cssId{s22}{= \frac{1}{3}}$
Use fraction names, not decimal names.
Use fraction names, not decimal names.
$\cssId{s24}{(-8)^{1/3}}
\cssId{s25}{= \root 3\of{-8}}
\cssId{s26}{= -2}$
$\displaystyle
\begin{align}
\cssId{s27}{(-8)^{-1/3}}\
&\cssId{s28}{= \frac{1}{(-8)^{1/3}}}\cr\cr
&\cssId{s29}{= \frac{1}{\root 3\of{-8}}}
\cssId{s30}{= \frac{1}{-2}}\cr\cr
&\cssId{s31}{= -\frac{1}{2}}
\end{align}$
$
\begin{align}
\cssId{s32}{16^{3/4}}\
&\cssId{s33}{= (16^{1/4})^3}\cr\cr
&\cssId{s34}{= (\root 4\of{16})^3}\cr\cr
&\cssId{s35}{= 2^3}
\cssId{s36}{= 8}
\end{align}
$
$\displaystyle
\begin{align}
\cssId{s37}{16^{-3/4}}\
&\cssId{s38}{= \frac{1}{16^{3/4}}}\cr\cr
&\cssId{s39}{= \frac{1}{(16^{1/4})^3}}\cr\cr
&\cssId{s40}{= \frac{1}{(\root 4\of{16})^3}}\cr\cr
&\cssId{s41}{= \frac{1}{2^3}}
\cssId{s42}{= \frac{1}{8}}
\end{align}
$
Practice
Feel free to use scrap paper and pencil to compute your answers. Do not use a calculator for these problems.
Input ‘nd’ if an expression is not defined.