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 $\,-x\,$

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

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.)