PRACTICE WITH RATIONAL EXPONENTS
by Dr. Carol JVF Burns (website creator)
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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.
$\cssId{s24}{(-8)^{1/3}} \cssId{s25}{= \root 3\of{-8}} \cssId{s26}{= -2}$
$\displaystyle \cssId{s27}{(-8)^{-1/3}} \cssId{s28}{= \frac{1}{(-8)^{1/3}}} \cssId{s29}{= \frac{1}{\root 3\of{-8}}} \cssId{s30}{= \frac{1}{-2}} \cssId{s31}{= -\frac{1}{2}}$
$\cssId{s32}{16^{3/4}} \cssId{s33}{= (16^{1/4})^3} \cssId{s34}{= (\root 4\of{16})^3} \cssId{s35}{= 2^3} \cssId{s36}{= 8}$
$\displaystyle \cssId{s37}{16^{-3/4}} \cssId{s38}{= \frac{1}{16^{3/4}}} \cssId{s39}{= \frac{1}{(16^{1/4})^3}} \cssId{s40}{= \frac{1}{(\root 4\of{16})^3}} \cssId{s41}{= \frac{1}{2^3}} \cssId{s42}{= \frac{1}{8}}$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Practice with $\,x\,$ and $\,-x\,$

Feel free to use scrap paper and pencil to compute your answers.
Do not use a calculator for these problems.
Simplify:

 (MAX is 22; there are 22 different problem types.)