Writing Rational Exponents as Radicals
Want some practice with the other direction? Writing Radicals in Rational Exponent Form
As long as everything is defined:
$$ \cssId{s7}{x^{p/q}} \cssId{s8}{= (x^p)^{1/q}} \cssId{s9}{= \root q\of{x^p}} $$ or $$ \cssId{s11}{x^{p/q}} \cssId{s12}{= (x^{1/q})^p} \cssId{s13}{= (\root q\of{x})^p}$$
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.
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Examples
Write in radical form:
Concept Practice
- Choose a specific problem type, or click ‘New problem’ for a random question.
- Think about your answer.
- Click ‘Check your answer’ to check!
On this exercise, you may assume that $\,x\,$ is positive, so that everything is defined.