WRITING RATIONAL EXPONENTS AS RADICALS

As long as everything is defined,

$\displaystyle x^{p/q} = (x^p)^{1/q} = \root q\of{x^p}$

or

$\displaystyle x^{p/q} = (x^{1/q})^p = (\root q\of{x})^p$

In both cases, the denominator in the exponent indicates the type of root.
The numerator in the exponent is a power, which can go either inside or outside the radical.

EXAMPLES:

Write in radical form:

$x^{1/2} = \sqrt{x}$
$x^{1/3} = \root 3\of {x}$
$x^{3/2} = \sqrt{x^3} = (\sqrt{x})^3$
$\displaystyle x^{-1/2} = \frac{1}{\sqrt{x}}$
$\displaystyle 3x^{-1/5} = \frac{3}{\root 5\of{x}}$
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 Rational Exponents

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
You may assume that $\,x\,$ is positive, so that everything is defined.
 Write in radical form:
 (MAX is 10; there are 10 different problem types.)