1. **State the problem:** We need to evaluate the expression $$n = \frac{1.65^2 \times 0.5 \times 0.5 \times 70}{70 \times 0.1^2 + 2.72^2 \times 0.3 \times 0.7}$$ 2. **Recall the order of operations:** Calculate powers first, then multiplication and addition. 3. **Calculate the numerator:** $$1.65^2 = 2.7225$$ $$\text{Numerator} = 2.7225 \times 0.5 \times 0.5 \times 70$$ Calculate step-by-step: $$2.7225 \times 0.5 = 1.36125$$ $$1.36125 \times 0.5 = 0.680625$$ $$0.680625 \times 70 = 47.64375$$ 4. **Calculate the denominator:** $$70 \times 0.1^2 = 70 \times 0.01 = 0.7$$ Calculate the second term: $$2.72^2 = 7.3984$$ $$7.3984 \times 0.3 = 2.21952$$ $$2.21952 \times 0.7 = 1.553664$$ Sum the denominator terms: $$0.7 + 1.553664 = 2.253664$$ 5. **Form the fraction:** $$n = \frac{47.64375}{2.253664}$$ 6. **Simplify the fraction:** $$n \approx 21.14$$ **Final answer:** $$n \approx 21.14$$