1. **State the problem:** Simplify the expression $\left(2^2 \cdot 5^2\right)^{\frac{1}{2}} \cdot 8^{\frac{1}{3}} \div \frac{1}{2} - 11$. 2. **Use the properties of exponents:** - $\left(a^m \cdot b^n\right)^p = a^{m p} \cdot b^{n p}$ - $a^{\frac{1}{2}} = \sqrt{a}$ - $a^{\frac{1}{3}} = \sqrt[3]{a}$ 3. **Simplify inside the parentheses:** $$\left(2^2 \cdot 5^2\right)^{\frac{1}{2}} = \left(4 \cdot 25\right)^{\frac{1}{2}} = 100^{\frac{1}{2}} = \sqrt{100} = 10$$ 4. **Simplify $8^{\frac{1}{3}}$:** $$8^{\frac{1}{3}} = \sqrt[3]{8} = 2$$ 5. **Rewrite the division by $\frac{1}{2}$ as multiplication by 2:** $$\div \frac{1}{2} = \times 2$$ 6. **Put it all together:** $$10 \cdot 2 \times 2 - 11$$ 7. **Calculate step-by-step:** $$10 \cdot 2 = 20$$ $$20 \times 2 = 40$$ $$40 - 11 = 29$$ **Final answer:** $29$