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Simplify : $$\frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{ of }}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{ of }}\frac{{28}}{5} - \frac{2}{3}}}{\kern 1pt} {\kern 1pt} = ?$$

Correct Answer: 2
$$\eqalign{ & {\text{According to question}} \cr & \frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{of}}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{of}}\frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{51}} \times \frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7} \times \frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{15}} - \frac{1}{3}}}{{\frac{2}{9} \times 4 - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{7}{9} - \frac{1}{3}}}{{\frac{8}{9} - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{{7 - 3}}{9}}}{{\frac{{8 - 6}}{9}}} \cr & \Rightarrow \frac{4}{2} \cr & \Rightarrow 2 \cr} $$

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?

$$\left( {\frac{{\sqrt {625} }}{{11}} \times \frac{{14}}{{\sqrt {25} }} \times \frac{{11}}{{\sqrt {196} }}} \right){\kern 1pt} $$     is equal to :

$${\text{If}}\,{\kern 1pt} {\left( {\frac{a}{b}} \right)^{x - 1}} = {\left( {\frac{b}{a}} \right)^{x - 3}},$$     then the value of x is

Simplify : $$\frac{{0.41 \times 0.41 \times 0.41 + 0.69 \times 0.69 \times 0.69}}{{0.41 \times 0.41 - 0.41 \times 0.69 + 0.69 \times 0.69}} = ?$$

Simplify : $$\frac{{{{1.5}^3} + {{4.7}^3} + {{3.8}^3} - 3 \times 1.5 \times 4.7 \times 3.8}}{{{{1.5}^2} + {{4.7}^2} + {{3.8}^2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 3.8 \times 1.5}}$$           = ?

$$\eqalign{ & {\text{The}}\,{\text{value}}\,{\text{of}} \cr & \frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}\,\text{is}: \cr} $$

The value of $$\left( {\frac{{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}}{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}} \right)$$       is :

The value of $${\text{ }}\root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} $$        is ?

The value of $$\left( {\frac{{0.943 \times 0.943 - 0.943 \times 0.057 + 0.057 \times 0.057}}{{0.943 \times 0.943 \times 0.943 + 0.057 \times 0.057 \times 0.057}}} \right)$$         is :