Practice with Rational Exponents

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Some typical examples are given below. For a complete discussion, read the text.
These ideas are also explored in these web exercises:
Writing Radicals in Rational Exponent Form
Writing Rational Exponents as Radicals

EXAMPLES:

$9^{1/2} = \sqrt{9} = 3$

$(-9)^{1/2} = \sqrt{-9} = \text{nd}$ Input “nd” if an expression is not defined.

$-9^{1/2} = -\sqrt{9} = -3$

$\displaystyle 9^{-1/2} = \frac{1}{9^{1/2}} = \frac{1}{\sqrt{9}} = \frac{1}{3}$ Use fraction names, not decimal names.

$(-8)^{1/3} = \root 3\of{-8} = -2$

$\displaystyle(-8)^{-1/3} = \frac{1}{(-8)^{1/3}} = \frac{1}{\root 3\of{-8}} = \frac{1}{-2} = -\frac{1}{2}$

$16^{3/4} = (16^{1/4})^3 = (\root 4\of{16})^3 = 2^3 = 8$

$\displaystyle 16^{-3/4} = \frac{1}{16^{3/4}} = \frac{1}{(16^{1/4})^3} = \frac{1}{(\root 4\of{16})^3} = \frac{1}{2^3} = \frac{1}{8}$

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.

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