As long as everything is defined,
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$\displaystyle x^{p/q} = (x^p)^{1/q} = \root q\of{x^p}$
or
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$\displaystyle x^{p/q} = (x^{1/q})^p = (\root q\of{x})^p$
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:
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$x^{1/2} = \sqrt{x}$
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$x^{1/3} = \root 3\of {x}$
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$x^{3/2} = \sqrt{x^3} = (\sqrt{x})^3$
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$\displaystyle x^{-1/2} = \frac{1}{\sqrt{x}}$
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$\displaystyle 3x^{-1/5} = \frac{3}{\root 5\of{x}}$
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.