<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-roots-as-exponents-ii">Roots as Exponents II Exercise</a></p><p>Sometimes writing <strong><span style="color:#27ae60;">Roots as Exponents</span></strong>, or vice versa, can be a bit tricky if we see something like the examples below.</p>
<p><span style="font-size:20px;"><span style="color:#8e44ad;">Examples</span></span></p>
<p>$$\sqrt{ab} = (ab)^{\frac{1}{2}} = a^{\frac{1}{2}}b^{\frac{1}{2}}$$</p>
<p>$$\sqrt[3]{a^2} = a^{\frac{2}{3}}$$</p>
<p>$$\sqrt[5]{x^3} = x^{\frac{3}{5}}$$</p>
<p>$$\sqrt[3]{x^9} = x^{\frac{9}{3}} = x^3$$</p>
<p>$$\sqrt[4]{x^4} = x^{\frac{4}{4}} = |x|$$</p>
<p>Note that the exponent under the radical (the square root thingy) becomes the numerator of the fraction and the number on top of the radical becomes the denominator.</p>