Al calcular las operaciones $\left ( \frac{18\times 25}{2^{3}\times 3^{1}\times 5^{2}} \right )^{\frac{1}{2}}$ el resultado es

 $$\left ( \frac{18\times 25}{2^{3}\times 3^{1}\times 5^{2}} \right )^{\frac{1}{2}}$$

$$=\left ( \frac{2\times 3^{2}\times 5^{2}}{2^{3}\times 3^{1}\times 5^{2}} \right )^{\frac{1}{2}}$$

$$=(2^{1-3}\times 3^{2-1}\times 5^{2-2})^{\frac{1}{2}}$$

$$=(2^{-2}\times 3^{1}\times 5^{0})^{\frac{1}{2}}$$

$$=2^{-2\times {\frac{1}{2}}}\times 3^{1\times {\frac{1}{2}}}\times 5^{0\times {\frac{1}{2}}}$$

$$=2^{-1}\times 3^{\frac{1}{2}}\times 5^{0}$$

$$=\frac{3^{\frac{1}{2}}}{2}$$

$$=\frac{\sqrt{3}}{2}$$