Section 1.3 : Radicals
3. Write the following expression in exponential form.
\[\sqrt[6]{{ab}}\] Show SolutionAll this problem is asking us to do is basically use the definition of the radical notation and write this in exponential form instead of radical form.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\left( {ab} \right)}^{\frac{1}{6}}}}}\]Be careful with parenthesis here! Recall that the only thing that gets the exponent is the term immediately to the left of the exponent. So, if we’d dropped parenthesis we’d get,
\[a{b^{\frac{1}{6}}} = a\left( {{b^{\frac{1}{6}}}} \right) = a\,\,\sqrt[6]{b}\]which is most definitely not what we started with. The only way to make sure that we understand that both the \(a\) and the \(b\) were under the radical is to use parenthesis as we did above.