Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 33

$c^\frac{1}{2}$

We are asked to replace radicals with exponents in the given equation: $\sqrt[4]{c^2}$ Recall the rational exponent property (pg. 382): $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$ Applying this property, we get: \begin{align*} \sqrt[4]{c^2}&=c^{\frac{2}{4}}\\ &=c^\frac{1}{2} \end{align*}