1. The problem is to convert the expression $\frac{2\pi^c}{9}$ into degrees. 2. Recall that $\pi$ radians equals 180 degrees. To convert radians to degrees, multiply by $\frac{180}{\pi}$. 3. The expression is $\frac{2\pi^c}{9}$ radians. To convert to degrees: $$\frac{2\pi^c}{9} \times \frac{180}{\pi}$$ 4. Simplify the expression: $$= \frac{2 \times 180 \times \pi^c}{9 \times \pi} = \frac{360 \pi^c}{9 \pi}$$ 5. Since $\pi^c = \pi^{c-1} \times \pi$, we can write: $$\frac{360 \pi^c}{9 \pi} = \frac{360}{9} \pi^{c-1} = 40 \pi^{c-1}$$ 6. Therefore, the expression in degrees is: $$40 \pi^{c-1}$$ This is the simplified degree measure of the given expression.