PRACTICE WITH RATIONAL EXPONENTS
 
EXAMPLES:
[beautiful math coming... please be patient] $9^{1/2} = \sqrt{9} = 3$
[beautiful math coming... please be patient] $(-9)^{1/2} = \sqrt{-9} = \text{nd}$     Input “nd” if an expression is not defined.
[beautiful math coming... please be patient] $-9^{1/2} = -\sqrt{9} = -3$
[beautiful math coming... please be patient] $\displaystyle 9^{-1/2} = \frac{1}{9^{1/2}} = \frac{1}{\sqrt{9}} = \frac{1}{3}$     Use fraction names, not decimal names.
[beautiful math coming... please be patient] $(-8)^{1/3} = \root 3\of{-8} = -2$
[beautiful math coming... please be patient] $\displaystyle(-8)^{-1/3} = \frac{1}{(-8)^{1/3}} = \frac{1}{\root 3\of{-8}} = \frac{1}{-2} = -\frac{1}{2}$
[beautiful math coming... please be patient] $16^{3/4} = (16^{1/4})^3 = (\root 4\of{16})^3 = 2^3 = 8$
[beautiful math coming... please be patient] $\displaystyle 16^{-3/4} = \frac{1}{16^{3/4}} = \frac{1}{(16^{1/4})^3} = \frac{1}{(\root 4\of{16})^3} = \frac{1}{2^3} = \frac{1}{8}$
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.)