﻿ Practice with Rational Exponents
PRACTICE WITH RATIONAL EXPONENTS
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

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
Practice with $\,x\,$ and $\,-x\,$