1. **State the problem:** Simplify the expression $\frac{2^5 \times 8}{16} \times 2$. 2. **Recall the rules:** Use the laws of exponents and basic arithmetic operations. 3. **Rewrite the expression:** $$\frac{2^5 \times 8}{16} \times 2$$ 4. **Express 8 and 16 as powers of 2:** $$8 = 2^3, \quad 16 = 2^4$$ 5. **Substitute these into the expression:** $$\frac{2^5 \times 2^3}{2^4} \times 2$$ 6. **Combine powers in numerator:** $$\frac{2^{5+3}}{2^4} \times 2 = \frac{2^8}{2^4} \times 2$$ 7. **Simplify the fraction using the rule $\frac{a^m}{a^n} = a^{m-n}$:** $$2^{8-4} \times 2 = 2^4 \times 2$$ 8. **Rewrite the multiplication:** $$2^4 \times 2^1$$ 9. **Add exponents when multiplying same bases:** $$2^{4+1} = 2^5$$ 10. **Calculate the final value:** $$2^5 = 32$$ **Final answer:** $32$