﻿ Practice with Rational Exponents

# Practice with Rational Exponents

These ideas are also explored in these web exercises: Writing Radicals in Rational Exponent Form and

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.
$\cssId{s16}{-9^{1/2}} \cssId{s17}{= -\sqrt{9}} \cssId{s18}{= -3}$
$\displaystyle \cssId{s19}{9^{-1/2}} \cssId{s20}{= \frac{1}{9^{1/2}}} \cssId{s21}{= \frac{1}{\sqrt{9}}} \cssId{s22}{= \frac{1}{3}}$
Use fraction names, not decimal names.
$\cssId{s24}{(-8)^{1/3}} \cssId{s25}{= \root 3\of{-8}} \cssId{s26}{= -2}$
\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.