1. **State the problem:** Simplify the expression $$2\pi^{1/2}(8 - 2t) \div 8\sqrt{\pi}$$. 2. **Recall the rules:** - $\pi^{1/2}$ is the same as $\sqrt{\pi}$. - Division of expressions means multiplying by the reciprocal. - Simplify constants and like terms carefully. 3. **Rewrite the expression:** $$\frac{2\pi^{1/2}(8 - 2t)}{8\sqrt{\pi}}$$ 4. **Replace $\pi^{1/2}$ with $\sqrt{\pi}$:** $$\frac{2\sqrt{\pi}(8 - 2t)}{8\sqrt{\pi}}$$ 5. **Cancel $\sqrt{\pi}$ in numerator and denominator:** $$\frac{2(8 - 2t)}{8}$$ 6. **Simplify the fraction:** $$\frac{2}{8} = \frac{1}{4}$$ 7. **Multiply the simplified fraction by $(8 - 2t)$:** $$\frac{1}{4}(8 - 2t) = \frac{8 - 2t}{4}$$ 8. **Simplify numerator if desired:** $$\frac{8}{4} - \frac{2t}{4} = 2 - \frac{t}{2}$$ **Final answer:** $$2 - \frac{t}{2}$$