1. The problem is to simplify the expression \( \sqrt[6]{c^6} \). 2. Recall that the sixth root of a number \( x \) is written as \( \sqrt[6]{x} = x^{\frac{1}{6}} \). 3. Applying this to \( c^6 \), we have \( \sqrt[6]{c^6} = (c^6)^{\frac{1}{6}} \). 4. Use the power of a power rule: \( (a^m)^n = a^{m\cdot n} \), so \( (c^6)^{\frac{1}{6}} = c^{6 \times \frac{1}{6}} = c^1 = c \). 5. Therefore, the simplified form of \( \sqrt[6]{c^6} \) is \( c \). Final answer: \( \boxed{c} \).