1. **State the problem:** Calculate the value of the expression $$\frac{(6.626 \times 10^{-34})^2}{2\pi \cdot (6.64 \times 10^{-29}) \cdot 298 \cdot (1.8 \times 10^{-23})}$$. 2. **Write the formula and explain:** We need to square the numerator and then divide by the product in the denominator. 3. **Calculate the numerator:** $$ (6.626 \times 10^{-34})^2 = 6.626^2 \times (10^{-34})^2 = 43.907876 \times 10^{-68} = 4.3907876 \times 10^{-67} $$ 4. **Calculate the denominator:** $$ 2\pi \cdot 6.64 \times 10^{-29} \cdot 298 \cdot 1.8 \times 10^{-23} $$ Calculate the constants first: $$ 2\pi \approx 6.283185 \quad \Rightarrow \quad 6.283185 \times 6.64 = 41.728 \quad \Rightarrow \quad 41.728 \times 298 = 12434.944 \quad \Rightarrow \quad 12434.944 \times 1.8 = 22382.8992 $$ Calculate the powers of ten: $$ 10^{-29} \times 10^{-23} = 10^{-52} $$ So denominator is: $$ 22382.8992 \times 10^{-52} = 2.23828992 \times 10^{-48} $$ 5. **Divide numerator by denominator:** $$ \frac{4.3907876 \times 10^{-67}}{2.23828992 \times 10^{-48}} = \frac{4.3907876}{2.23828992} \times 10^{-67 - (-48)} = 1.961 \times 10^{-19} $$ 6. **Final answer:** $$ \boxed{1.96 \times 10^{-19}} $$ This is the value of the given expression.